probability question4

explorer

2012-02-15 9:07 pm

Problem 4:
A by-election is being held to fill 5 seats in a council that have recently
become vacant. A total of 9 candidates have registered to run in the elec-
tion. The candidates can be divided into 3 groups based on their political
aliations with: 4 in Group A, 3 in Group B, and 2 in Group C.

(a) In how many ways can a voter choose 5 candidates?
(b) In how many ways can a voter choose 5 candidates such that at least
3 candidates from Group A are chosen?
(c) In how many ways can a voter choose 5 candidates such that at least
1 candidate from each group is chosen?

回答 (1)

用戶2053

2012-02-17 12:23 am

✔ 最佳答案

a)9C5 = 126 ways
b)3 from GroupA ways * 2 from other 5 ways
+ 4 from GroupA ways * 1 from other 5 ways= 4C3 * 5C2 + 4C4 * 5C1= 4 * 10 + 1 * 5= 45 ways
c) All ways - Group A ,B only ways - Group B ,C only ways - Group C ,A only ways= 126 - (4+3)C5 - (3+2)C5 - (2+4)C5= 126 - 7C5 - 5C5 - 6C5= 126 - 21 - 1 - 6= 98 ways

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