Here is the 8th grade POW:
Draw six cards from a standard deck of 52 playing cards without replacement. How many distinct ways can you choose these six cards so that:
1) The first card drawn is a spade,
2) the second card drawn is also a spade,
3) the third card drawn is a club,
4) the fourth card drawn is a diamond,
5) the fifth card drawn is a red card (either a diamond or a heart), and
6) the sixth and final card drawn is an ace?
27 comments:
A.H.
If you want to play a spade, a spade, a club, a diamond, a red card, and an ace in that order, you have to calculate how many possibilities there are. To do this, you must multiply the number of cards of the certain type that are left in the deck by each other. Here is how it goes:
#1 - 13 spades possible because there are 13 cards of each type in a deck
#2 - 12 spades possible because youv'e already used one
#3 - 13 clubs possible because there are thirteen in a deck
#4 - 13 diamonds possible because there are thirteen in a deck
#5 - 25 reds possible because it covers 2 types, but youv'e already used 2
#6 - 4 aces possible because there are 4 aces in a deck
If you multiply each set by the next value, you get this:
12 x 13 = 156
156 x 13 = 2028
2028 x 13 = 26364
26364 x 25 = 659100
659100 x 4 = 2636400
So the total possibilities that you can get this combination is 2636400 times :)
Submitted by A.H.
IW
1-13 possible
2-12 possible
3-13 possible
4-13 possible
5-25 possible
6-1-4 possible
13
X12
156
X13
2028
X13
26364
X25
659100
X4 x3 x2 x1 x0
2636400|1977300|1318200|659100|0
I multiplied 13 times 12 because it shows how many possible ways for the first 2
then i multiplied the answer of that, 156, times 13 for possible ways for 3
i multiply that answer, 2028, by 13 for possible ways of 4
then i muliply that answer, 26364 because there is 25 reds left for answer of 5
then i multiply that, 659100, by 4,3,2,1 and 0 because at max there is 4 aces left and minimum 0.
that gives the answer for number 6.
so the answer is(unsimplified) then 2,636,400 ways to do it,
1,977,300 ways, 1,318,200 ways, 659,100 or 0 ways
simplified it is
1 out of every 2,636,400 tries you can do it
1 out of every 1,977,300 tries you can do it
1 out of every 1,318,200 tries you can do it
1 out of every 659,100 tries you can do it, or
it may be impossible if you already used up all of your aces.
then you would add them all up to find total avaible tries- 7,250,100 tries. so it is
1 out of every 7,250,100 tries you can do the 'magic trick'.
IW
There are 13 cards of each type in a deck. So that means 26 of those are red and 13 are spades lets begin, you can draw the first spade in 13 different ways, the second spade can be drawn in 12 different ways so that’s because you have already drawn one of the first 13 spades, so now you have 156 different ways. Now you have to draw a club, and there is 13 clubs 156 times 13 equals 2028, now you have to draw a diamond there are also 13 diamonds 13 times 2028 equals 26364, ok now we need to draw a red card there are 26 red cards in a deck, but we already drew one so we have 25 to chose from 26364 times 25 equals 659100, ok now we have to draw one of the four ace there is a chance that you drew one or two of them, but there is a chance that we drew one of the aces from the deck already so you could either end up with 659100 times 3 659100 times 2 times 4 or times 1 but the maximum amount of card combinations you can get is 2636400.
E.H.
RW
4
3
14
14
27
2
127008
To find out how many different ways there is to do what the steps say u need to multiply how many of each one with the other
4 spades times the 3 spades left over
Times 14 clubs times the 14 diamonds,
Times 27(there are 14 hearts left and 13 diamonds)
And times the two aces left
Equaling 127008<---- answer
A.H.
If you want to play a spade, a spade, a club, a diamond, a red card, and an ace in that order, you have to calculate how many possibilities there are. To do this, you must multiply the number of cards of the certain type that are left in the deck by each other. Here is how it goes:
#1 - 13 spades possible because there are 13 cards of each type in a deck
#2 - 12 spades possible because youv'e already used one
#3 - 13 clubs possible because there are thirteen in a deck
#4 - 13 diamonds possible because there are thirteen in a deck
#5 - 25 reds possible because it covers 2 types, but youv'e already used 2
#6 - 4 aces possible because there are 4 aces in a deck
If you multiply each set by the next value, you get this:
12 x 13 = 156
156 x 13 = 2028
2028 x 13 = 26364
26364 x 25 = 659100
659100 x 4 = 659100 x 3 659100 x 2 659100 x 1
2636400 + 1977300 + 1318200 + 659200
For a total of 7,250,100
So the total possibilities that you can get this
combination is 7,250,100 times :)
Submitted by A.H.
Ms
52 cards
4 suits
13 cards/suit
1)probability=1/52 odds are 13 to 52
2)probability=1/51 odds are 12 to 51
3)probability=1/50 odds are 13 to 50
4)probability=1/49 odds are 13 to 49
5) probability=1/48 odds are 25 to 48
6) probability=1/47 odds are 13 to 47
A.L. 8th grade
There are 13 cards of each suit...
13 spades
13 hearts
13 clubs
13 diamonds
This makes thirteen possiblities of drawing a card of each suit...
Draw 1)-13 possible chances
Draw 2)-12 possible chances
Draw 3)-13 possible chances
Draw 4)-13 possible chances
Draw 5)-25 possible chances
Draws 1) 4) 6) Possible chances
13*12=156
156*13=2028
2028*13=26364
26264*25=659100
659100*4=2636400
*4=2636400 *3=1977300 *2=1318200 *1=6519100
*0= (of Course) 0
add these all together...
The Information above For the First draw, there are 13 possible chances of drawing a spade.
Multiply this by the chances of drawing a spade on the second draw (13), and so far there are 156 chances of this occurance happening. Going through the Process of multplying each chance of drawing the cards indicated, Overall, There are 2636400 chances of all of these cards being drawn in this order. But, there are a few more steps, multpily your totals by 4, 3, 2, 1 ,and 0 for each chance of already drawing and Ace. Overall, there are 7,250,100 possible ways for this to happen.
In ratio, there is a 1 out of every 1208350 chance of cards being drawn in this order.
K.B
The probability of drawing an spade on your first card is one out of four. This is because Spades are one out of the four suits in a deck. This makes a one out of four.
The chance of you then drawing another spade is twelve out of fifty one. This is because there are fifty one cards left and twelve spades.
Then drawing a spade is a thirteen out of fifty. There are fifty cards left and thirteen clubs. You took another card last time and there is still all of the clubs.
Then there is a forty nine out of thirteen chance of then drawing a Diamond. This is also because there are forty nine cards and thirteen diamonds.
The chances of then drawing a red are fifteen out of forty eight. There are forty eight cards and fifteen red cards left.
Then you have a chance of four out of forty seven. If you have all ready drawn an ace you have a three out of forty seven. If you have drawn two aces you have a two out of forty seven. If you have drawn three you have a one out of forty seven. If you have drawn all of the aces there is no chance.
DGT
There are an extremely large amounts of ways to do this problem. The way that I got my answer was by doing the problem 13x12x13x13x25x4, the first each number in the problem represents another step in the problem. The answer I got for my problem, meaning how many ways there are to solve it, would be 2,636,400.
AM
There are 13 cards of each type in a deck. So that means 26 of those are red and 26 are black. You can draw the first spade in 13 different ways, the second spade can be drawn in 12 different ways so that’s because you have already drawn one of the first 13 spades, so now you have 156 different ways. Now you have to draw a club, and there is 13 clubs 156 times 13 equals 2028, now you have to draw a diamond. There are 13 diamonds 13 times 2028 equals 26364, ok now we need to draw a red card there are 26 red cards in a deck, but we already drew a diamond so we have 25 to chose from 26364 times 25 equals 659100, ok now we have to draw one of the four ace there is a chance that you drew one or two of them, but there is a chance that we drew one of the aces from the deck already so you could either end up with 659100 times 3 659100 times 2 times 4 or times 1 but the maximum amount of card combinations you can get is 2636400. The equation for this is 13x12x13x25x4.
E.H.
There are 13 cards of each type in a deck. So that means 26 of those are red and 13 are spades lets begin, you can draw the first spade in 13 different ways, the second spade can be drawn in 12 different ways so that’s because you have already drawn one of the first 13 spades, so now you have 156 different ways. Now you have to draw a club, and there is 13 clubs 156 times 13 equals 2028, now you have to draw a diamond there are also 13 diamonds 13 times 2028 equals 26364, ok now we need to draw a red card there are 26 red cards in a deck, but we already drew one so we have 25 to chose from 26364 times 25 equals 659100, ok now we have to draw one of the four ace there is a chance that you drew one or two of them, but there is a chance that we drew one of the aces from the deck already so you could either end up with 659100 times 3 659100 times 2 times 4 or times 1 but the maximum amount of card combinations you can get is 2636400.
An equation for this would be 13X12X13X13X25X4
CT
If the first card you had drawn was a spade, there would be a 25% possibility that you would get a spade.
If the second card was also a spade, then it would be 12/51 of a possibility that you could draw it.
When picking the third card, there is a 26% that you would draw a club.
For picking the fourth card, there would be a 13/49 chance that you would pick a diamond.
If you were to pick a red card that is either a heart or a diamond, the probability of picking would be 4/45.
Finally, if you had the chance to pick an ace, you could have the probability of 4/41.
I got my probabilities because I found how many of that certain card there was in the deck. Then I wrote a ratio on how many cards it was out of. As the number of possibilities decrease and increase, the total amount of cards started to decrease. I subtracted a card from the total number of cards after every ratio.
I didn’t really understand how to get the correct answers. I do not think that I was heading in the right direction and I felt that the answers that people were getting weren’t making any sense.
E.Ma
1. The first thing I did was to figure out the chances of drawing the certain card for the certain step. I figured out that there were 13 chances a spade could be drawn on the first card
13 cards 25/100
2. Next I figured out the chance that a spade could be drawn on the second step. There was twelve because a spade was already picked on the step before.
12 cards 23/100
3. There were still 13 clubs that could be drawn.
13 cards 25/100
4. There is also still 13 diamonds left to pick.
13 cards 25/100
5. For this one I had picked a red diamond before this step so there could only be 25 cards that could possibly be picked
25 cards 48/100
6. There would still be four aces left so there are four opportunities to pick an ace.
4 cards 7/100
The next thing I did was multiply all of the cards that could be picked
13x12x13x13x25x4=2636400
That means that there is are 2636400 different ways that the combination could happen.
JB
13X12X13X13X25X4
=2636400
RS
If the first card you draw out of the 52 card deck is a spade, then the probability of drawing a spade would be 13/52 or 1/4. If the second card you draw is also a spade, sinc the first card is gone it would be 12/51. If the third card you draw is a club, then since the first and second cards are gone the probability would be 13/50. If the fourth card you draw is a diamond, since you already took out the first, second, and third cards, the probability would be 13/49. if the fifth card you draw is any red card, and since the only red card that has already been picked is a diamond, the probability would be 25/48. The final card that you would pick would be an ace, and since there are only four aces in the deck, the probability would be 4/46 or 2/23. The total number of times this would happen would be 1/2,409,264 and I know you told me this was close but it wasn't right but we ran out of time in class. right now it was between 2,190,240 and 2,409,264.
KG
52/4=13
4 aces
13 spades 13 clubs 13 diamonds 13 hearts
26 red 26 black
13/52=1/4
¼ chance spade or 25/100
23/100 chance another spade
¼ chance club or 25/100
¼ chance diamond or 25/100
48/100 chance of red card
7/100 chance of ace
The first thing I did was find out how many cards of each suite were in a deck of 52. Then I divided that number into 52 to check it and there were 13 cards of each suite. There are 4 aces, 26 red cards, and 26 black cards. There was a ¼ chance of drawing a spade for the first card. The second card drawn was also a spade and had a 23/100 chance of being another spade. The third card drawn, a club had a ¼ chance of being drawn. The fourth card was a diamond and had a ¼ chance of being drawn. The fifth card could be a red card so there was a 48/100 chance of being drawn. The last card was an ace so it had a 7/100 chance of being drawn
K.T.
1) First you have to draw an spade.
2) You have a ¼ chance of getting that.
3) Then you have to get another spade and theres a 12 out of 51 chance that you will get that.
4) Then you would have to draw a club out of 50 cards and there are 13 clubs.
5) Then you would have to draw a diamond out of 49 cards and there are 13 diamonds so you have about 13/49 chance to get it.
6) Then you need to get a red card and there are 25 red cards left and there are 48 total cards left.
7) The odds of getting a red card is 1 out of 23.
8) Finally, you must draw an ace and there are 4 aces and only 47 cards left and there is a 1 and 11.75 chance that you would draw an ace.
9) So all in all, I say its nearly impossible to do all of that.
K.T.
1) First you have to draw an spade.
2) You have a ¼ chance of getting that.
3) Then you have to get another spade and theres a 12 out of 51 chance that you will get that.
4) Then you would have to draw a club out of 50 cards and there are 13 clubs.
5) Then you would have to draw a diamond out of 49 cards and there are 13 diamonds so you have about 13/49 chance to get it.
6) Then you need to get a red card and there are 25 red cards left and there are 48 total cards left.
7) The odds of getting a red card is 1 out of 23.
8) Finally, you must draw an ace and there are 4 aces and only 47 cards left and there is a 1 and 11.75 chance that you would draw an ace.
9) So all in all, I say its nearly impossible to do all of that.
CK
This POW was to find out how many ways you could draw these six cards out of a deck of 52. The first two cards are spades; the third is a club, then a diamond, fifth a red card (heart or diamond) and last an ace. First you draw 1/13 spades leaving 1/12 for you to draw next. Next 1/13 clubs is drawn; then 1/13 diamonds. For the fifth card, a red heart or diamond, you only have 24/26 cards to draw from since you have already drawn a diamond and can no longer draw an ace sine your last card is an ace. So 1/24 red hearts or diamonds is drawn. Lastly, ¼ aces is drawn. To figure out how many possible ways you can draw these cards I multiplied 13x12x13x13x24x4 which equals 2,530,944.
AR
The POW was to find out how you could get a certain six cards out of a deck of fifty-two cards.
Those cards were:Spade,Spade,Club,Diamond,Red (heart or diamond), and an Ace
Then, what you do to find your probability you would multiply 13x12x13x13x24x4 you do this for the 13 spades, then next you get 12 for the rest of the spades because you can’t pick a spade you already used then 13 for the clubs then 13 for the diamonds then 24 for the red cards. You have 24 because you already used one red diamond and then for the ace you pick at the end. Then, finally you multiply that by 4 for the four aces. And then you get your probability which is: 2,530,944. You would have a 2,530,944 probability of picking those certain six cards out of a deck of fifty-two cards.
M.G.
This week our P.O.W. wanted us to figure out the probability for each set of cards in a deck of fifty-two cards.
The first step was to figure out how many cards there were in each suit and the answer was there are 13 cards in each suit. There are also 4 aces. It says you have to get a spade, spade, club, diamond, a red card either a diamond or heart and an ace and you can’t replace the card. So there are 13 spades then when you pick a spade again you can’t get 13 so you would 12, there are 13 clubs, 13 diamonds and 24 red cards and 4 aces. There are 24 red cards because you already picked a diamond so it would be 12+12 which equals 24. Then you would multiply 13*12*13*13*24*4=2636400. You multiply the numbers together because to find probability for each set you have to find the highest number. You would multiply 4 in the equation because there are 4 aces. So my final answer was 2636400.
JJ
What I did was I knew that the first card had to be a spade and I knew that there are 13 spades in a deck.
13
Then I saw that the second number had to be a spade and since the first spade was drawn I knew that there was 12 more spades.
13*12=156
After that it said that the third card had to be a club and there are 13 clubs in the deck.
13*12*13=2028
The fourth card has to be a diamond and there are 13 possible diamonds.
13*12*13*13=26364
The fifth card had to be a red card either a heart or diamond, and there are 13 of each suit but one diamond is already drawn so there are 25 possibilities.
13*12*13*13*25=659100
The last card had to be an ace, and there is one ace of each suit.
13*12*13*13*25*4=2636400
That’s my final answer
E. mU.
Prob Prob% Odds Odds%
13/52 25% 13/39 33%
12/51 24% 12/39 31%
13/50 26% 13/37 35%
13/49 27% 13/36 36%
25/48 52% 25/23 109%
4/47 9% 4/42 10%
2,636,400 chances
We got 2,636,400 chances by multiplying all the numerators of the probabilities together. When you have 3 types of meat and 3 types of bread, to find the total possibilities of how many types of sandwiches you multiply 3*3=9. There are 9 different sandwich possibilities. Knowing that, I multiplied all of the numerators of the probabilities/odds. 13*12*13*13*25*4= 2,636,400. After asking Ms. Leckman, I know this answer is very close to the correct answer, I have found many different answers like, 2,409,800 or something like that.
D.M.
Our problems of the week asked us to find the total number of chances that we had for certain cards were chosen out of a 52 card deck. The first thing I did was wrote all the problems out in a fraction for probability. The probabilities went, 13/52 12/51, 13/50, 13/49, 25/48, and 4/47. I thought it would be smart if I took the approach and multiplied them all together because they would equal the total number of chances put together. Example- 3 types of bread and 3 types of meat. You would multiply to get 9 chances. I got 2,636,400. That is what my answer for the POW is this week.
K.A.
13/52
12/51
13/50
13/49
25/48
4/47
I don’t know the answer but I do know that it’s between 2,230,800-2,416,700 and I somehow got 2,284,880 and that’s what I’m going to stick with. Hope it’s right =]
My final answer is 2,284,880. I multiplied all the numerators together and just plugged in some other numbers close to the actual numerator to try and get the answer. Unfortunately I still didn’t even get the right answer, but I think the reason all of my answers are wrong is because the possibility of getting an ace is random because with the other cards one of them could b an ace. ITS JUST NOT FAIR =[. thanks
CVDV
First I found the probability
13/52
12/51
13/50
13/49
25/287
4/47
Then I found the odds
13/39
12/39
13/37
13/36
25/23
4/43
Then I multiplied the odds
13/39
156/1521
2028/56277
26364/2025972
659100/4597356
Then I fount that tall the odds multiplied together was:
2636400/2003686308
d.c.
52 cards
13 spades
13 clubs
13 aces
13 hearts
1) 13 there are 13 spades
2) 13x12=156 there are 12 spades left so you would add that to it
3) 13x12x13=2028 there 13 clubs so you would add that to the problem
4) 13x12x13x13=26324 there are 13 diamonds in the deck so you would at that to the problem
5) 13x12x13x13x2=632736 ½ of the cards are red so I added that to the problem
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