HMMT 2014 C2

There are 10 people who want to choose a committee of 5 people among them. They do this by first electing a set of $1,2,3$, or 4 committee leaders, who then choose among the remaining people to complete the 5 -person committee. In how many ways can the committee be formed, assuming that people are distinguishable? (Two committees that have the same members but different sets of leaders are considered to be distinct.)