SOLUTION: If a pair of dice is rolled, in how many ways are the two numbers different? If three dice are rolled, in how many ways are at least two of the dice the same?

Question 1000962: If a pair of dice is rolled, in how many ways are the two numbers different? If three dice are rolled, in how many ways are at least two of the dice the same?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The dice have 36 outcomes.
6 of them are the same: 1,1;2,2;3,3;4,4;5,5;6,6
the other 30 are not.
For 3 dice, there are 216 outcomes.
at least two means two or three are the same.
three occurs 36 in 216 times. That is (1/6)(1/6)(1/6)*6 for each number (1/6)-111,222,333,444,555,666
Suppose the first die is a 1: two occur (1/6)(1/6)(5/6)*3, because there are 3 ways the two can occur.
That is 15/216. But that can occur for each of the six numbers. The probability is 90/216 that exactly two will occur, and the probability 96/216, or 6/13.
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