Question

A committee of 6 persons is to be formed from 8men and 10 women. Find the number of ways in which committee contains 1- at least 2men 2-at most 4women​

Answer 1

Step-by-step explanation:

Without considering the demand of the 2 men, the total number of committees

=

10

C

3

.

7

C

3

+

10

C

4

.

7

C

2

=8610 (two cases: 3 women, 3 men, and 4 women, 2 men)

If we select the two particular men in the committee, the remaining 4 members can be selected in

10

C

3

.

5

C

1

+

10

C

4

.

5

C

0

=810 (two cases: 3 women, 1 man, and 4 women, 0 men)

∴ The number of committees in which they work together =810

∴The number of committees in which they do not work together =8610−810=7800