Question

in how many ways can a committee consisting of four ladies and 3 gentleman be formed from 10 ladies and 6 gentleman what will be the number if Mrs X refuses to serve in a committee having Mr y as a member​

Answer 1

Answer:

3 ladies out of 8 can be selected in

8

C

3

ways and 4 gentlemen out of 7 in

7

C

4

ways.

Now each way of selecting 3 ladies is associated with each way of selecting 4 gentlemen.

Hence, the required number of ways =

8

C

3

×

7

C

4

=56×35=1960.

We now find the number of committee of 3 ladies and 4 gentlemen in which both Mrs X and Mr Y are member.

In this case we can select 2 other ladies from the remaining 7 in

7

C

2

ways and 3 other gentlemen from the remaining 6 in

6

C

3

ways.

∴ The number of ways in which both Mrs X and Mr Y are always included =

7

C

2

×

8

C

3

=21×20=420

Hence the required number of committee in which Mrs X and Mr Y do not serve together =1960=420=1540