In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women ?

246

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222

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186

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None of these

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Solution

The correct option is A
246

Required number of ways

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

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