Choosing a Committee In how many ways can a committee of four be chosen from a group of ten if Barry and Harry refuse to serve together on the same committee?

To find:

The number of ways by which a committee of four is chosen.

Given:

A committee of four is to be chosen from a group of ten and Barry and Harry does not serve on the same committee.

Approach:

The number of combinations of n distinct objects taken r at a time is,

C(n,r)=n!r!(n−r)!    ;  (r≤n)

Calculation:

The number of ways by which four is chosen from a group of ten is given as,

C(10,4)=10!4!(10−4)!=10×9×8×7×