Question

From 10 people how many ways are there to select a committee consisting of a chairman, vice-chair, and three other committee members?

Answer 1

total number of people =10

So initially chairman can be selected in 10 ways.

vice-chair can be selected in 10-1=9 ways (as chairman post is taken by 1 out of those 10)

3 other commitee members can be taken out of the remaining 8 people in 8C3 ways

That is

So the total number of ways in which commitee can be formed is

Hence the total number of ways of forming a commitee is 5040.

Thank you !!