Kristy 發問於 科學及數學數學 · 6 年前

Finite Math Question

A certain board of directors consists of 15 people. Three subcommittees are to be formed: a Finance subcommittee of 5 people, a Programs subcommittee of 4 people and a Fundraising subcommittee of 6 people. Each board member must sit on exactly 1 subcommittee, and the Treasurer (Mr. Bucks) must be on the Finance subcommittee. In how many ways can the subcommittees be chosen?

1 個解答

評分
  • Adam
    Lv 7
    6 年前
    最愛解答

    • Choose the Treasurer (Mr. Bucks) into the Finance subcommittee(C(1,1)).

    • From the rest 14 people, choose 4 into the Finance subcommittee (C(14, 4)).

    • From the rest 10 people, choose 4 into the Programs subcommittee (C(10,4)).

    • Choose the rest 6 people into the Fundraising subcommittee (C(6,6))

    Number of ways the subcommittees can be chosen

    = C(1,1) × C(14!/4!) × C(10,4) × C(6,6)

    = 1 × (14!/4!10!) × (10!/6!4!) × 1

    = 14!/4!6!4!

    = 210210

    資料來源: wongmanadam
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