Question

If $n$ identical dice are rolled, then number of possible outcomes are

• A. $6^n$
• B. $\frac{6^n}{n!}$
• C. ${}^{n+5}{C}_5$
• D. None of these

Answer 1

The correct option is C ${}^{n+5}{C}_5$

Since dice are 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 $(x+x^2+x^3+x^4+x^5+x^6{)}^n.$

That is ${}^{n+6-1}{C}_{6-1}$

The possible outcomes after rolling n identical dice equivalent to ${}^{n+5}{C}_5$