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A committee of 3 is to be formed from 6 men and 4 women

  1. How many ways can a committee of 3 be formed?
  2. How many ways can a committee of 3 men be formed?
  3. what is the probability that the committee is made up of only men?
  4. how many can a committee of 2 men and 1 women be formed?
  5. what is the probability that the committee is made up of 2 men and 1 woman?
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A) 3 of 10 is ${10 \choose 3}=\frac{10.9.8}{3.2.1}=10.3.4=120$.

B) 3 of 6 is ${6 \choose 3}=\frac{6.5.4}{3.2.1}=5.4=20$.

C) The probability that a committee is of 3 men is 20/120=1/6.

D) Two men and one woman can be chosen in ${6 \choose 2}{4 \choose 1}=\frac{6.5} {2.1}\frac{4}{1}=15.4=60$.

E) The probability is 60/120=1/2.

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