Question 1190744
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A committee of 4 people is to be selected from a group of 5 men and 7 women. If the selection
is made randomly, what is the probability the committee will consist of 2 men and 2 women
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<pre>
5 + 7 = 12 people.


In all,  {{{C[12]^4}}} = {{{(12*11*10*9)/(1*2*3*4)}}} = 495 combinations are possible of 12 people taken 4 at a time.


It is the full size of the space of events in this problem.


Of them,  {{{C[5]^2*C[7]^2}}} = 10*21 = 210 quadruples consists of two men and two women: they are favorable quadruples in this problem.


THEREFORE, the probability under the problem's question is


    P = {{{favorable/total}}} = {{{210/495}}} = {{{14/33}}} = 0.4242... = 0.4242 = 42.42%   (rounded).    <U>ANSWER</U>
</pre>

Solved.