SOLUTION: A committee consisting of 3 men and 4 women is to be choose at random from 5 women and 6 men. What is the probability that one particular women and man will be on it.

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Question 1202956: A committee consisting of 3 men and 4 women is to be choose at random from 5 women and 6 men. What is the probability that one particular women and man will be on it.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

"Choose" the one particular man and one particular woman and put them on the committee.

There are 4 women and 5 men left, from which you need to choose 2 men and 3 women: C(4,3)*C(5,2) = 4*10 = 40

The total number of ways of choosing the last 5 members of the committee out of the remaining 9 people without restrictions is C(9,5) = 126

ANSWER: 40/126 = 20/63

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Revised answer after seeing the response from tutor @ikleyn....

The above solution only makes sure that one particular man and one particular woman have to be on the committee; it overlooks the fact that the committee must contain 3 men and 4 women.

Total number of ways of choosing 3 of the 6 men and 4 of the 5 women is

C(6,3)*C(5,4) = 20*5 = 100

So the answer to the question is 40/100 = 2/5 = 40% = 0.4

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
A committee consisting of 3 men and 4 women is to be choose at random
from 5 women and 6 men.
What is the probability that one particular woman and man will be on it.
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        My solution and my answer are different from that by @greenestamps.

The number of all favorable possible committees consisting of 3 men and 4 women, satisfying the imposed restrictions is favorable = = 10*4 = 40 (the same number as provided in the solution by @greenestamps). The number of all possible committees consisting of 3 men and 4 women without restrictions on one particular woman and man is total = = 20*5 = 100 (this number is different from the value in solution by @greenestamps). The answer is the ratio P = = = = = 0.4 = 40%.

Solved.