A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. The probability that you have 1 cherry candy and 2 lemon candies is

Question

anonymous · Answer

This is a bit more difficult than usual because it is sampling without replacement.  Say you pick 1 lemon on the first try, then there is only 1 lemon left and also the total changes, so the probabilities change.

order:  CLL
P = 6/11 times 2/10 times 1/9 = 12 / 11 x 10 x 9
order: LCL
P = 2/11 times 6/10 times 1/9 = 12 / 11 x 10 x 9
order: LLC
P = 2/11 times 1/10 times 6/9 = 12 / 11 x 10 x 9

We have (12 + 12 + 12) / 11 X 10 X 9
 = 36/990