1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A. 564 B.645
C. 735 D.756
E. None of these
Answer: Option D
Explanation:
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways
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= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
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=
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7 x 6 x 5
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x
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6 x 5
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+ (7C3 x 6C1) + (7C2)
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3 x 2 x 1
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2 x 1
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= 525 +
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7 x 6 x 5
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x 6
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+
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7 x 6
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3 x 2 x 1
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2 x 1
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= (525 + 210 + 21)
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= 756.
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