SOLUTION: Please help... A committee of four is selected from seven men and six women. Find the probability that there is at least one of each gender on the committee. The answer should b

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Question 1095712: Please help...
A committee of four is selected from seven men and six women. Find the probability that there is at least one of each gender on the committee.
The answer should be 133/143, but I got it wrong.
Thank you.
Answer by KMST(5347) About Me  (Show Source):
You can put this solution on YOUR website!
With 7+6=13 people, you can form 13%2A12%2A11%2A10%2F%282%2A3%2A4%29 committees of 4 people.
Among those there are the only 7%2A6%2A5%2A4%2F%282%2A3%2A4%29 made of all men,
and the only 6%2A5%2A4%2A3%2F%282%2A3%2A4%29 made of all women.
The other committees have at least one person of each gender.
Those are
%2813%2A12%2A11%2A10-7%2A6%2A5%2A4-6%2A5%2A4%2A3%29%2F%282%2A3%2A4%29=%2813%2A4%2A3%2A11%2A5%2A2-%286%2A5%2A4%29%287%2B3%29%29%2F%282%2A3%2A4%29=%2813%2A11%2A6%2A5%2A4-6%2A5%2A4%2A11%29%2F%282%2A3%2A4%29=
of the total ={{143*6*5*4/(2*3*4}}} .
The probability is the ratio of those two quantities,
133%2A6%2A5%2A4%2F%28143%2A6%2A5%2A4%29=highlight%28133%2F143%29 .

If you got 139%2F143 the mistake was that
13%2A12%2A11%2A10-7%2A6%2A5%2A4-3%2A6%2A5%2A4
is equal to
and not to 13%2A12%2A11%2A10-%287-3%29%2A6%2A5%2A4 .