SOLUTION: A group consists of 15 people: 5 Americans, 6 Canadians and 4 Mexicans. (a) In how many ways can a sub-group of 4 people be selected? (b) In how many ways can a

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Question 710195: A group consists of 15 people: 5 Americans, 6 Canadians and 4 Mexicans.
(a) In how many ways can a sub-group of 4 people be selected?






(b) In how many ways can a sub-group of 4 people consist of all Canadians?
Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!

A group consists of 15 people: 5 Americans, 6 Canadians and 4 Mexicans.
(a) In how many ways can a sub-group of 4 people be selected?
(5+6+4 people CHOOSE 4) = (15 people CHOOSE 4) =  C(15,4) = 1365 ways.

(b) In how many ways can a sub-group of 4 people consist of all Canadians?
(6 Canadians CHOOSE 4) = C(6,4) = 15 ways

(c) In how many ways can a sub-group of 4 people consist of 2 Canadians and 2
Mexicans? 
(6 Canadians CHOOSE 2) times (4 Mexicans CHOOSE 2) = C(6,2)·C(4,2) = 15·6 = 90 ways

Edwin
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