1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# 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:

A

(a) 1960

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

(b) 1540

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

(c) 3240

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

(d) None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## 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.

Suggest Corrections
7
Join BYJU'S Learning Program
Related Videos
Fundamental Principle of Counting
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program