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?

Question

Accepted Answer

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

∴ Required number of ways

= (⁷C₃ x ⁶C₂) + (⁷C₄ x ⁶C₁) + (⁷C₅)

=	❨	7 x 6 x 5	x	6 x 5	❩	+ (⁷C₃ x ⁶C₁) + (⁷C₂)
		3 x 2 x 1		2 x 1

= 525 +	❨	7 x 6 x 5	x 6	❩	+	❨	7 x 6	❩
		3 x 2 x 1					2 x 1

= (525 + 210 + 21)

= 756.

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?

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