SOLUTION: 3. A group consists of 4 men and 3 women. a) In how many ways can 3 people be selected from the group of 7? b) In how many ways can 3 people be selected if they are all men?

Algebra ->  Probability-and-statistics -> SOLUTION: 3. A group consists of 4 men and 3 women. a) In how many ways can 3 people be selected from the group of 7? b) In how many ways can 3 people be selected if they are all men?      Log On


   

Question 628526: 3. A group consists of 4 men and 3 women.
a) In how many ways can 3 people be selected from the group of 7?
b) In how many ways can 3 people be selected if they are all men?
c) What is the probability that the selected group will be all men?
Answer by nerdybill(7384) About Me  (Show Source):
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3. A group consists of 4 men and 3 women.
a) In how many ways can 3 people be selected from the group of 7?
7C3
= 7!/3!(7-3)!
= 4!(5*6*7)/3!4!
= (5*6*7)/3!
= (5*6*7)/(1*2*3)
= (5*6*7)/(2*3)
= (5*6*7)/(6)
= (5*7)
= 35
.
b) In how many ways can 3 people be selected if they are all men?
4C3
= 4!/3!(4-3)!
= 4!/3!1!
= 4!/3!
= 3!(4)/3!
= 4
.
c) What is the probability that the selected group will be all men?
4/35 = 0.11 = 11%