SOLUTION: A city council consists of five Democrats and six Republicans. If a committee of four people is​ selected, find the probability of selecting two Democrats and two Republicans. (T

Algebra ->  Permutations -> SOLUTION: A city council consists of five Democrats and six Republicans. If a committee of four people is​ selected, find the probability of selecting two Democrats and two Republicans. (T      Log On


   

Question 1132412: A city council consists of five Democrats and six Republicans. If a committee of four people is​ selected, find the probability of selecting two Democrats and two Republicans. (Type a fraction. Simplify your answer.)
Answer by greenestamps(13200) About Me  (Show Source):
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Number of ways to choose 2 of the 5 democrats and 2 of the 6 republicans: (5 choose 2) times (6 choose 2).

Number of ways of choosing 4 of the 11 council members: 11 choose 4.

ANSWER: %28C%285%2C2%29%2AC%286%2C2%29%29%2FC%2811%2C4%29+=+%2810%2A15%29%2F330+=+150%2F330+=+5%2F11

NOTE: You can get good practice in this type of calculations by performing the similar calculations for all the possible combinations of democrats and republicans and verify that the sum of the probabilities for all possible combinations is equal to 1.