SOLUTION: A committee of eight Congressmen will be selected from a group of nine Democrats and seven Republicans. Find the number of ways of obtaining a committee with exactly three Democrat

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Question 1146054: A committee of eight Congressmen will be selected from a group of nine Democrats and seven Republicans. Find the number of ways of obtaining a committee with exactly three Democrats.
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
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The committee = 3 Democrats + 5 Republican.


(1)  You can select 3 democrats from 9 democrats in  C%5B9%5D%5E3 = %289%2A8%2A7%29%2F%281%2A2%2A3%29 = 84 ways.


(2)  You can select 8-3 = 5 Republican for remaining 5 positions from 7 Republicans in  C%5B7%5D%5E5 = %287%2A6%29%2F%281%2A2%29 = 21 ways.



(3)  Selections (1) and (2) are independent;  therefore, the total number of obtaining the committee 

     is the product  84*21 = 1764.    ANSWER

Solved.