Question

Consider a collection of envelopes consisting of 3 red envelopes​, 1 blue envelope​, 3 green envelopes​, and 2 yellow envelopes. If three envelopes are selected at​ random, without​ replacement, determine the probability that they are all green envelopes.

Answer 1

Total envelopes: 3 + 1 + 3 + 2 = 9 with a total of 3 green ones.

Probability of picking green first: 3 out of 9 = 3/9 = 1/3

There are 8 envelopes left, with 2 green ones.

Probability of picking a green one is 2 out of 8 = 2/8 = 1/4

There are 7 envelopes left and 1 green one.

Probability of picking green is 1 out of 7 = 1/7

Probability of picking all 3 = 1/3 x 1/4 x 1/7 = 1/84