What is the probability that two of the marbles are red when drawn?

Question

A bag contains 9 red marbles, 7 white marbles, and 7 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? Can you show me how you solved it?

Answer 1

23 total marble, 9 red - probability red on first draw = 5/19

22 total marbles, 8 red - probability red on 2nd draw = 4/11

21 total marbles, 7 red, probability red on 3rd draw = 1/3

20 total marbles, 6 red, probability red on 4th draw = 3/10

19 total marbles, 5 red, probability red on 5th draw = 5/19

probability all 5 marbles drawn are red is the product of the above 5 probabilities.