From a group of 7 men and 6 women 5 persons are to be selected to form a committee so that at least 3 men are in a committee. In how many ways can this be done.
Case 1: 3 men: 7 C 3 * 6 C 2 = 525
Case 2: 4 men: 7 C 4 * 6 C 1 = 210
Case 3: 5 men: 7 C 5 = 21
525 + 210 + 21 = 756.
+876 (73)(62)+(74)(61)+(75)=35⋅15+35⋅6+21=7⋅(75+30+3)=7⋅108=756
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