Question
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 ?
Answer: Option D
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we may have ( 3 men and 2 women ) or ( 4 men and 1 women ) or ( 5 men only )
`:.` Required number of ways = `( 7_ ( C _ 3) xx 6 _ (C _ 2)) + (7 _ (C _ 4) xx 6 _ (C _ 1)) + (7 _ (C _ 5))`
= `((7 xx 6 xx 5)/(3 xx 2 xx 1) xx (6 xx 5)/(2 xx 1)) + (7_ (C _3) xx 6 _ (C _1)) + (7 _ (C _ 2))`
=`525 + ((7 xx 6 xx 5)/(3 xx 2 xx 1) xx 6) + ( (7 xx 6)/(2 xx 1))`
= (525 + 210 + 21) = 756.
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