If $k$ identical six-sided dice are thrown, and $n$ identical coins are tossed, how many results can be distinguished?

Question

I'm being ask this combinatorics question:

"If $k$ identical six-sided dice are thrown, and $n$ identical coins are tossed, how many results can be distinguished?"

I found that there are $\binom{k+5}{5}$ distinguished results for the dice. However, I'm not sure how to combine them with the distinguished results for the coins.

Thank you so much for helping!

Answer 1

Note that a coin is really just a 2 sided die in your question

Therefore:

$${k+5 \choose 5} * {n+1 \choose 1} = {k+5 \choose 5} * (n+1)$$

If "s" is the number of sides of the dice in question the general form for any group of fair dice is: $${n+(s-1) \choose s-1} $$