Out of 5 men and 2 women, a committee of 3 members is to be formed. In how many ways can it be formed if the committee c

Question

Out of 5 men and 2 women, a committee of 3 members is to be formed. In how many ways can it be formed if the committee contains at least one woman?

Accepted Answer

Total persons = 7. Total ways to form a committee of 3 members is $^7C3 = 35$. The number of ways with no woman (i.e., all 3 are men) is $^5C3 = 10$. Ways with at least one woman = Total ways - Ways with no woman = $35 - 10 = 25$. Therefore, option B is correct.

Permutations and Combinations

❓ Sibling Questions in this Chapter