Q. From a group  of 7 men and 6 women , 5 persons  are to be selected to form a committee so that atleast 3 men are there on the committee . In how many can it be done ?

1.
Case 1: The comittee has 5 men5 men can be selected out of 7 men in C57 waysNumber of ways of forming committee=C57=21Case 2: The committee has 4 men and 1 women4 men can be selected out of 7 men in C47 ways1 woman can be selected out of 6 women in C16 waysNumber of ways of forming committee=C47×C16=210Case 3: The committe has 3 men and 2 women3 men can be selected out of 7 men in C37 ways2 women can be selected out of 6 women in C26 waysNumber of ways of forming committee=C37×C26=525Total number of ways of forming the committee=21+210+525=756
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