Dattaprabhakar G. answered • 07/27/14

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Campbell:

A total of 10 members, 6 men and 4 women. A committee of 3 can be chosen in

^{10}C_{3}total ways. This is the denominator of your probability calculations.The (composite) event "at least 2 women on the committee" consists of "exactly 2 women out of 4 -and 1 man out of 6-", "exactly 3 women and 0 men".

The required probability is {(

^{4}C_{2})(^{6}C_{1}) + (^{4}C_{3})(^{6}C_{0})} /(^{10}C_{3}). The calculation can be done manually and easily, but I want you to practice using the "binomial coefficients calculator" available as the following web-lnk:http://www.zweigmedia.com/RealWorld/tutstats/bincoeffs.html

When you open this link, scroll to the bottom of the page. NOTE THE SPECIAL CASES, one you use above. Now you are not scared of calculating any quantity of the type

^{n}C_{r}. Right?Dattaprabhakar ("Dr.G.")