Question

Six women and seven men are on the faculty in a history department at a school.(a)How many ways are there to the select a committee of five members of the department if atleast one woman is on the committee.(b)How many ways are there to the select a committee of five members of the department ifthere are exactly 3 women on the committee.

Answer 1

1266,420

Explanation:

given that six women and seven men are on the faculty in a history department at a school.

women Men

6 7

To be selected 5 members

a) There should be atleast one woman

No of ways to have atleast one woman = Total ways to select 5 members - no of ways that no woman is selected

=
`13C5-7C5`

(Because all members are selected from 7 men only)

= 1266

b) Exactly 3 women then no of men 2

So 3 from 6 women and 2 from 7 men to be selected

No of ways =
`6C3 (7C2)\\=(20) 21\\=420`