If I have 4 dices (1-6) how many possibilities do I have to get exactly one 2? So for example a combination of 2, 3, 2, 4 is not possible.
My solution was: 4 * 5^3.
Thx :D
Dice Combinatorics
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combinatorics
discrete-mathematics
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0Yes, that works. For posting with mathematical expressions, see [this introduction](http://math.stackexchange.com/help/notation). – 2017-01-23
1 Answers
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Assuming the dice are of different colors, first one picks the location of the $2$ (in 4 ways) and then fills the other 3 outcomes with any non-2 values, so your solution is correct: $$ 4 \times 5^3 = 500. $$
If the dice are identical, you have to account for the fact that the above argument counts e.g. 2,4,3,4 and 2,3,4,4 twice, when it is in reality one combination.