Question 1175829
<br>
The total number of ways of choosing 4 of the 12 people is<br>
{{{C(12,4) = 495}}}<br>
The number of ways of choosing 4 of the 5 men and 0 of the 7 women is<br>
{{{(C(5,4)*C(7,0)) = 5*1 = 5}}}<br>
So the probability of choosing 4 men is 5/495.<br>
The number of ways of choosing 2 of the 4 men and 2 of the 4 women is<br>
{{{(C(5,2)*C(7,2)) = 10*21 = 210}}}.<br>
So the probability of choosing 2 men and 2 women is 210/495.<br>
Simplify the two answers if needed.<br>
When you are first learning to solve problems like this, you can get further practice and also get confirmation that your calculations are correct by finding the probabilities of all other combinations of men and women and verifying that the sum of all the probabilities is 1.<br>
3 men and 1 woman: {{{C(5,3)*C(7,1) = 10*7 = 70}}}; probability 70/495<br>
1 man and 3 women: {{{C(5,1)*C(7,3) = 5*35 = 175}}}; probability 175/495<br>
0 men and 4 women: {{{C(5,0)*C(7,4) = 1*35 = 35}}}; probability 35/495<br>
Sum of all the probabilities: (5+70+210+175+35)/495 = 495/495 = 1<br>