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From 7 men and 4 ladies a committee of 6 is to be formed. In how many ways can this be done when the committee contains1. exactly two ladies.2. at least two ladies. |
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Answer» 1. Exactly two ladies can be selected from 4 in 4C2 = \(\frac{4 \times 3}{1 \times 2}\) = 6. The remaining 4 should be selected from 7 men in 7C4 = \(\frac{7 \times 6 \times 5 \times 4}{1 \times 2 \times 3 \times 4}\) = 35. The required number of ways = 6 × 35 = 210. 2. At least 2 ladies can be selected as follows;
The required number of ways = 210 + 140 + 21 = 371. |
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