How many groups of 5 with a given group leader can be selected from 12 people?

Question

Out of 12 people, only 2 groups of 5 can be formed

My answer: C(12,5) = 792

I feel like my answer might be incorrect because 1 of the 5 people should be a leader. Does this change anything?

Answer 1

Once you chose the $5$ people for the group you need to choose who is the leader. You have $5$ options to choose him, so multiply your answer by $5$. The answer is $792\times5=3960$.

Answer 2

The number $\binom{12}5$ is the number of ways of choosing groups of $5$ people from a pool of $12$.

You can choose the leader first ($12$ possibilities) and the remaining team after ($\binom{11}4$ possibilities). Thereby, the answer is $12\times\binom{11}4=3\,960$.