Question 867569
There are 19+19 = 38 people total. So there are 38 C 11 = 1,203,322,288 ways to form a committee of 11 people (with no restrictions on gender). 



I'm using the <a href="http://www.mathwords.com/c/combination_formula.htm">combination formula</a> to compute 38 C 11. It's faster to do with a calculator, but I recommend you do a few by hand to get an idea of how it works.


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a)


There are 19 C 6 = 27,132 ways to pick 6 men (from a pool of 19 men)



There are 19 C 5 = 11,628 ways to pick 5 women (from a pool of 19 women)



There are 27,132*11,628 = 315,490,896 ways to pick a committee of 11 people where there are 6 men and 5 women.



Divide this by the total number of ways to form an 11 member committee: 315,490,896/1,203,322,288 = 0.26218320656586



Then round to two decimal places: 0.26218320656586 ----> <font color="red">0.26</font>



So the probability of selecting exactly 6 men and 5 women is <font color="red">0.26</font>



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b) 



There are 19 C 11 = 75,582 ways to pick a committee of all women.



Divide this by the total number of ways to form an 11 member committee: 75,582/1,203,322,288 = 0.00006281110286



Then round to seven decimal places: 0.00006281110286 ----> <font color="red">0.0000628</font>



So the probability of selecting all women, ie a committee of 11 women, is <font color="red">0.0000628</font>