PLEASE HELP WITH THIS PROBABILITY QUESTION

Question

An Ice Chest Contains Six cans of apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice.  Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

Answer 1

Chest contains 20 cans. Chances of selecting apple=6/20; grape=8/20; orange=4/20; mango=2/20.

Initial chance of not selecting grape=12/20.

First can not grape: 12/20, 19 cans left.

Second can not grape: 11/19, 18 cans left.

Third can not grape: 10/18, 17 cans left.

Combined probability: 12*11*10/(20*19*18)=11/57=19.3%.