Question

In the U.S. Senate, there are 21 members on the Committee on Banking, Housing, and Urban Affairs. Nine of these 21 members are selected to be on the Subcommittee on Economic Policy. How many different committee structures are possible for this subcommittee?

Answer 1

₂₁C₉ = 293930

Explanation:

9 members out of 21 senators will be selected on the subcommittee on Economy Policy

So we are in case of combinations of 21 people in groups of 9

₂₁C₉ =21! /( (21-9)!) *9! ⇒21*20*19*18*17*16+15*14*13*12! /(21-9)! *9!

=21*20*19*18*17*16*15*14*13/ 9! ⇒ = 19*2*17*15*14*13/6 ⇒ =293930