Question 5927: If I roll 5 regular dice out of a cup, what is
1. The probability that I will get 5 of a kind. I think the answer is 1 in 1296.
2. What is the probability that I will get two pair, i.e., 22335, 55422, even 33433 would count as two pair. I come up with 1 in 34.56 rolls but I don't think this is correct.
Thanks,
Bob Boose
Found 2 solutions by khwang, pratapdas:
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! There are 5 possible numbers of a kind,the prob. is 5/6^5 = 5/1296 (use math notation, not regular English)
Among 5 dices, 2 of them are the same number, then 2 of the remaining 3 are
te same, the fifth one shouldbe different from the preevious two numbers.
There are 6*C(5,2)*5*C(3,2)*4 = 6*10*5*3*4 = 3600
So the prob. of 2 pairs is 3600/6^5 = 100/6^3 = 25/54 (use fraction
no decimals)
Kenny
Answer by pratapdas(1)  (Show Source):
You can put this solution on YOUR website! 1. There are 6 possibilities to get 5 of a kind on 5 regular dices, i.e. all 1, all 2, all 3, all 4, all 5, and all 6. Each one has a probability of 1/6^5. Therefore, total prob. = 6/6^5 = 1/6^4 = 1/1296.
2. We choose 2 dices among 5 (5C2), 1 value among 6 to place on those 2 dices (6C1), then we choose 2 dices from the rest 3 (3C2), and again 1 value from rest 5 to place on those 2 dices (5C1), and lastly 1 value among rest 4 to put on the last dice (4C1)
Total count = 5C2 * 6C1 *3C2 * 5C1 * 4C1 = 7200
Prob = 7200/6^5 = 25/27
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