marbles and boxes permutations

Question

In how many ways can five marbles can be dropped in six different boxes? Case (1) marbles are identical Case (2) marbles are distinct. I know this belongs to permutation and I don't know which formula I should adopt

Answer 1

If the marbles are identical, then we can use stars and bars to obtain $$ {n+k-1\choose k-1}={5+6-1\choose 6-1}=252. $$ If they are distinct, then the number of ways is given by $$ k^n=6^5=7776. $$