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匿名 發問於 科學及數學數學 · 5 年 前

Permutations and Combinations

1. 12 applicant remain in the last phase of a scholarship application, where 5 of them are boys and 7 of them are girls. Mr. Lee plans to invite 3 boys and 4 girls for individual interviews next week, and thus he is going to make a list according to the ordering of interviews. Find the possible number of lists to be made according to each of the following conditions.

(a) Select any 3 boys and 4 girls.

(b) The boys should be interviewed successively.

(c) Any two boys should not be interviewed successively.

1 個解答

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  • 5 年 前
    最佳解答

    1a) 5C3 * 7C4 * 7!= 1764000

    1b) 5C3 * 7C4 * 4! * 5C1 * 3!= 252000

    1c) 5C3 * 7C4 * 4! * 5C3 * 3!= 504000

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