Question 867360
There are 15+18 = 33 people total. So there are 33 C 11 = 193,536,720 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 33 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 15 C 8 = 6,435 ways to pick 8 men (from a pool of 15 men)



There are 18 C 3 = 816 ways to pick 3 women (from a pool of 18 women)



There are 6,435*816 = 5,250,960 ways to pick a committee of 11 people where there are 8 men and 3 women.



Divide this by the total number of ways to form an 11 member committee: 5,250,960/193,536,720 = 0.02713159549258



Then round to two decimal places: 0.02713159549258 ----> <font color="red">0.03</font>



So the probability of selecting exactly 8 men and 3 women is <font color="red">0.03</font> 



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b) 



There are 18 C 11 = 31,824 ways to pick a committee of all women.



Divide this by the total number of ways to form an 11 member committee: 31,824/193,536,720 = 0.00016443391208



Then round to seven decimal places: 0.00016443391208 ----> <font color="red">0.0001644</font>



So the probability of selecting all women, ie a committee of 11 women, is <font color="red">0.0001644</font>