Quantitative Reasoning

Permutation & Combination

Medium

A committee of 5 members is to be formed by selecting out of 6 men and 4 women. In how many different ways the committee can be formed if it should have at least 2 women?

120

180

186

181

✅ Correct Option: 3

Count by number of women:

2W, 3M: $\binom{4}{2}\binom{6}{3}=6\times20=120$ .

3W, 2M: $\binom{4}{3}\binom{6}{2}=4\times15=60$ .

4W, 1M: $\binom{4}{4}\binom{6}{1}=6$ .

Total $=120+60+6=186$ .

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Solution