A bag contains 8 red marbles, 7 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?

Answer 1

There are 8+7+8 = 23 marbles, 8 of which are red.

Then, without regard to order, the number of ways you can select 5 red marbles is C(8,5), and the number of ways you can select any marble is C(23,5), so the probability of selecting 5 red marbles is

C(8,5)/C(23,5) = 56/33649 = 8/4807 = .001664.