Question

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?

Answer 1

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

Answer 2

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%.