Posted by Katia on .
my problem is:
From the box containing 5 red balls, 7 blue balls, 10 black balls. you select 4 balls
what is the probabilty that EXACTLY 2 balls are black.
i know that you start it/set it up like this:
c(10,2)c(2,1) divided by c(22,4)
and i can get the answer by plugging it in the calculator. but i would like to know how to solve it by hand. help?

Math 
Reiny,
I answered it for you here
http://www.jiskha.com/display.cgi?id=1292286864
to evaluate without a calculator ? Wow
C(10,2) = 10!/(8!2!) = 10*9/2 = 45
C(12,2) = 12!/(10!2!) = 12*11/2 = 66
C(22,4) = 22!/(18!4!) = 22*21*20*19/(4*3*2*1) = 7315
You sure you want to do this "by hand" ?