Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them?

1/64

1/56

3/32

3/28

E2020 answer is 3/28

There are a total of 8 cards on the stack with two 1's, two 2's, three 3's and one four. For the first case, the probability of pulling 3 from the stack is 3/8. The situation is that there is no replacement such that on the second case, the number of cards on the stack is only 7. The probability of picking 2 out of the stack is 2/7. The overall probability is the product of the probabilities of the first and second case. Thus, the answer is 3/28.