I have 7 chocolate and 5 vanilla candies in a bag and 3 pieces are taken out.
What is the probability that 1 is chocolate and 2 are vanilla.

First we calculate the numerator of the probability, which is the number of
ways to succeed.

There are C(7,1) ways to choose the 1 chocolate and for each of 
those ways, there are C(5,2) ways to choose the 2 vanillas.

So the numerator of the probability is C(7,1)(C(5,2) = 7×10 = 70 ways.

The denominator is the number of ways to select ANY three, or C(12,3) = 220.

So the desired probability is 70 ways out of 220, or  = .

Edwin