SOLUTION: 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

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: 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       Log On

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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
Answer by khwang(438) About Me  (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