Q3. The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed to form a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee of which Mr. Y is a member is:
Q3. The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed to form a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee of which Mr. Y is a member is:
The correct option is
A 1540
3 ladies out of 8 can be selected in 8C3 ways and 4 gentlemen out of 7 in 7C4 ways. Now, each way of selecting 3 ladies is associated with each way of selecting 4 gentlemen. Hence, the required no. of ways. =8C3 x 7C4 = 56 x 35 = 1960.
We now find the number of committees of 3 ladies and 4 gentlemen in which both Mrs X and Mr Y are members.
In this case, we can select 2 other ladies from the remaining 7 in 7C2 ways and 3 other gentlemen from the remaining 6 in 6C3 ways. The no. of ways in which both Mrs X and Mr Y are always included = 7C2 x 8C3 = 21 x 20 = 420. Hence, the required number of committees in which Mrs X and Mr Y do not serve together = 1960 – 420 = 1540.
The correct option is
A 1540
3 ladies out of 8 can be selected in 8C3 ways and 4 gentlemen out of 7 in 7C4 ways. Now, each way of selecting 3 ladies is associated with each way of selecting 4 gentlemen. Hence, the required no. of ways. =8C3 x 7C4 = 56 x 35 = 1960.
We now find the number of committees of 3 ladies and 4 gentlemen in which both Mrs X and Mr Y are members.
In this case, we can select 2 other ladies from the remaining 7 in 7C2 ways and 3 other gentlemen from the remaining 6 in 6C3 ways. The no. of ways in which both Mrs X and Mr Y are always included = 7C2 x 8C3 = 21 x 20 = 420. Hence, the required number of committees in which Mrs X and Mr Y do not serve together = 1960 – 420 = 1540.
