Question 1202956
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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 {{{highlight(cross(women))}}} <U>woman</U> and man will be on it.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;My solution and my answer are different from that by @greenestamps.



<pre>
The number of all favorable possible committees consisting of 3 men and 4 women,
satisfying the imposed restrictions is

    favorable = {{{C[5]^2*C[4]^3}}} = 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     = {{{C[6]^3*C[5]^4}}} = 20*5 = 100  (this number is different from
                                        the value in solution by @greenestamps).


The answer is the ratio

    P = {{{favorable/total}}} = {{{40/100}}} = {{{4/10}}} = {{{2/5}}} = 0.4 = 40%.
</pre>

Solved.