Combinations

Question

A bag contains 50 marbles: 20 red, and 10 each of blue, green, and yellow; I reach into the bag and pick 5 marbles (simultaneously) at random. Determine the probability that my pick ... (a) consists of 2 red, 2 blue, and 1 of a third color. (b) includes at least 2 red marbles. (c) consists of 2 marbles of one color, 2 of another color, and 1 of a third color.

Answer 1

I did this on Excel just to make sure. There are 1024 total possibilities (4 choices, 5 picks, i.e., 4^5 possibilities).

a) 2 R, 2 B, a third color: 60 solutions so the probability is 60/1024 = 15/256

b) At Least 2 Red: 376 solutions so the probability is 376/1024 = 47/128

c) 2 of one color, 2 of another and 1 of a third: 360 solutions so the probability is 360/1024 = 45/128