Answer to Question #293933 in Discrete Mathematics for Tege

Question

How many outcomes are obtained from rollings n indistinguishable dice ?

Answer 1

Solution:

Since dice are indistinguishable (identical), so number of arrangements are possible like 2,3,4,5,6,1 and 1,3,2,4,5,6 will be considered as same outcome.

So number of possible outcome is simply the number of terms in the expansion of $\left(x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}\right)^{n}$ .

That is ${ }^{n+6-1} C_{6-1}$

The possible outcomes after rolling n identical dice equivalent to ${ }^{n+5} C_{5}$