Question

From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. In how many ways can the committee be formed if one man and one woman refuses to serve tog

Answer 1

910

Explanation:

From the given information;

Suppose that everyone served together;

Then, we have:

= C(8,3) × C(6,3)

=
`(8!)/(3!(8-3)!)* (6!)/(3!(6-3)!)`

=
`(8!)/(3!(5)!)* (6!)/(3!(3)!)`

= 1120

But since 1 man and 1 woman refuses to serve together;

Then:

The combination will be:

= C(7,2) × C(5,2)

=
`(7!)/(2!(7-2)!)* (5!)/(2!(5-2)!)`

=
`(7!)/(2!(5)!)* (5!)/(2!(3)!)`

= 210

∴

1120-210 = 910

Thus, the number of ways committee can be formed = 910