Question

From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

(a) 686

(b) 438

(c) 732

(d) 549

This question was posed to me during a job interview.

This interesting question is from Counting in section Counting of Discrete Mathematics

Answer 1

The correct answer is (a) 686

Explanation: We may have (2 men and 3 women) or (1 men and 4 woman) or (5 women only). The Required number of ways = (^8C2 × ^6C3) + (^8C1 × ^6C4) + (^6C5) = 686.