Finite Math Question
2014-10-15 9:16 pm
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?
回答 (1)
2014-10-16 2:34 am
✔ 最佳答案
• 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
參考: wongmanadam
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