There are six empty purses on the table. What is the number of ways to put 12 identical 1 rupee coin in purse such that at most one purse remains empty.
The way I did is
Case 1: No purse remains empty. In that case the answer should be $\binom{11}{5}$
Case 2: One purse remains empty. In this case answer should be $6\cdot \binom{11}{4}$
So the answer should be $\binom{11}{5} + 6\cdot \binom{11}{4}$
But the answer given is $\binom{12}{5} + 6\cdot \binom{11}{4}$
I believe the answer is wrong. Kindly verify.