probability

[kov82]

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In how many ways can 10 candidates (5 men 5 women) be elected for 3 vacancies of which 1 vacancy is reserved for a female candidate?

the answer is 110, can someone explain how using the P or C equations?

 

[Streetwolf]

In how many ways can 10 candidates (5 men 5 women) be elected for 3 vacancies of which 1 vacancy is reserved for a female candidate?

the answer is 110, can someone explain how using the P or C equations?

2 men, 1 woman
1 man, 2 women
3 women

Those are your possibilities.
In order of those above, we have:

(5 C 2)(5 C 1) = 10*5 = 50
(5 C 1)(5 C 2) = 5*10 = 50
(5 C 3) = 10

Total is 50 + 50 + 10 = 110.

 

[kov82]

thanks man, CDP math sucks at explaining this stuff