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    Question

    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?
    A 2416 Correct Answer Incorrect Answer
    B 2487 Correct Answer Incorrect Answer
    C 2318 Correct Answer Incorrect Answer
    D 2416 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Case I: ┬а 4 boys and 3 girls can be selected, Number of ways of selection =┬а8C4┬а├Ч┬а6C3┬а= 70 ├Ч 20 = 1400 Case II: 5 boys and 2 girls can be selected, Number of ways of selection =┬а8C5┬а├Ч┬а6C2┬а= 56 ├Ч 15 = 840 Case III: 6 boys and 1 girl can be selected, Number of ways of selection =┬а8C6┬а├Ч┬а6C1┬а= 28 ├Ч 6 = 168 Case IV: 7 boys can be selected, Number of ways of selection =┬а8C7┬а= 8 So, total number of ways of selecting the children = 1400 + 840 + 168 + 8 = 2416 ways

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