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In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?

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120

186

246

308

answer is C.

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Detailed Solution

Forming a committee with at least 1 woman. The possibilities are
●       1 woman and 4 men
●       2 women and 3 men
●       3 women and 2 men
●       4 women and 1 man
The number of ways they can be selected

C_{1}^{4} C_{4}^{6} + C_{2}^{4} C_{3}^{6} + C_{3}^{4} C_{2}^{6} + C_{4}^{4} C_{1}^{6} = 4 \times 15 + 6 \times 20 + 4 \times 15 + 1 \times 6 = 60 + 120 + 60 + 6 = 246

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