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

1/52.

Explanation:

The first friend's chance of picking a cotton shirt = 7/16, then the second one has a chance of 6/15 and so on ...

So the required probability is

7/16 * 6/15 * 5/14 * 4/13

= 840 / 43680

= 1/52.

Answer 2

Explanation:

There are total 16 sweatshirts.

Now the probability that first friend will get the cotton sweatshirt
`=(7)/(16)`

probability that the second friend wiil get the cotton sweatshirt
`=(6)/(15)`

similarly,

probability that the third and fourth friend will get the cotton sweatshirt

`=(5)/(14) and (4)/(13)`

Therefore, the probability that the friends order only cotton sweatshirt
`=(7)/(16) (6)/(15) (5)/(14) (4)/(13)`
`=(840)/(175500)`