7 children are to be selected from a group of 8 boys and 6 girls. In how many ways will the children with at most 3 girls and at least 4 boys be selected?
Case I: 4 boys and 3 girls can be selected, Number of ways of selection = 8C4 × 6C3 = 70 × 20 = 1400 Case II: 5 boys and 2 girls can be selected, Number of ways of selection = 8C5 × 6C2 = 56 × 15 = 840 Case III: 6 boys and 1 girl can be selected, Number of ways of selection = 8C6 × 6C1 = 28 × 6 = 168 Case IV: 7 boys can be selected, Number of ways of selection = 8C7 = 8 So, total number of ways of selecting the children = 1400 + 840 + 168 + 8 = 2416 ways
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