Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 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?

There are 16 sweatshirts in total.

7 of which are cotton.

There are 4 friends.

Say they all choose cotton sweatshirts,

First friend: (7/16)

Second friend: (6/15)

Third friend: (5/14)

Fourth friend: (4/13)

As you can see, there is a deduction in total number of sweatshirts available to be chosen and also in the total number of cotton sweatshirts available to be chosen.

Multiply these together = (7/16) * (6/15) * (5/14) * (4/13)

= 0.01923076923 = 1.92%

1.92% is the probability all friends order cotton sweatshirts

If you wanna estimate the probability of an event to happen, you have to multiply the probability of success of all the situations involved.

- Probability to get the first sweatshirt made of cotton: 7 of 16.

- Probability for the second one: 6 of 15, because there's one shirt less, and one cotton less.

- Prob for the third: 5 of 14

- Prob for the fourth: 4 of 13

So the probability to get four cotton shirts is: 7/16·6/15·5/14·4/13 = 0'019, something that could be rounded to 2%.