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Combination with Restrictions

Out of 7 men ...

Question

Out of 7 men and 4 women a committee of 5 is to be formed. The number of ways in which this can be done so as to include 2 women is

210

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220

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230

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240

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Solution

The correct option is D 210
Required number of ways $=$ selection of 2 women out of 4 and 3 men out of 7 $=^{4} C_{2} \times^{7} C_{3} = 6 \times 35 = 210$

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