SOLUTION: A team of 5 is to be chosen from 4 men and 5 women to work on a special project. i. In how many ways can the team be chosen? ii. In how many ways can the team be chosen to includ

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Question 450055: A team of 5 is to be chosen from 4 men and 5 women to work on a special project.
i. In how many ways can the team be chosen?
ii. In how many ways can the team be chosen to include just three women?
iii. What is the probability that the team includes just 3 women?
iv. What is the probability that the team includes atleast 3 women?
v. What is the probability that the team includes more men than women?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Note: as order is not important, these are solved using Combinations:

     nCx = n%21%2F%28x%21%28n-x%29%21%29

A team of 5 is to be chosen from 4 men and 5 women to work on a special project

i. In how many ways can the team be chosen? 9C5 = 126 ways

ii. In how many ways can the team be chosen to include just three women?

              5C3*4C2 = 10*6 = 60 ways

iii. What is the probability that the team includes just 3 women? 60/126

iv. What is the probability that the team includes at least 3 women?

  P(at least 3 women) = 1 - P(0 women ) -P(1 women ) -P(2 women )

                      = 1 - (0  - 5C1*4C4 - 5C2*4C3) / 9C5

v. What is the probability that the team includes more men than women?

   P(more men than women) = P(4men) + p(3men) = (5C1*4C4+ 5C2*4C3)/9C5