Each of four friends orders a sweatshirt from a catalog. There are 15 colors of sweatshirts, 5 of which are all cotton and 10 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?

1/5

12/65

1/273

11/5

The answer is 1/273. For the first friend, the probability of choosing one cotton sweatshirt is 5/15. For the second one, they need to choose different color. So the total amount and available amount both decrease one. The same method to third and forth person. So the final probability is (5/15) * (4/14) * (3/13) * (2/12) = 1/273.