Each of four friends orders a sweatshirt from a catalog. there are 18 colors of sweatshirts, 6 of which are all cotton and 12 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?

A91 divided by 15.
B77 divided by 255.
C1 divided by 204.
D1 divided by 15.

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)

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 Link

JeanaShupp JeanaShupp · Answer 2 · 2019-03-15T02:09:04-04:00

Answer: c. 1 divided by 204.

Step-by-step explanation:

Given: The number of friends = 4

The total number of sweatshirts =18

If each one orders a different color (no repeats) at random., then the total number of ways to order sweatshirts =\(^{18}P_4=\frac{18!}{(18-4)!}=\frac{18\times17\times16\times15\times14!}{14!}=73440\)

If the friends order only cotton sweatshirts, then the number of ways to order sweatshirts=\(^6P_4=\frac{6!}{(6-4)!}=\frac{6\times5\times4\times3\times2!}{2!}=360\)

Now, the probability that the friends order only cotton sweatshirts =\(\frac{360}{73440}=\frac{1}{204}\)

Hence, the probability that the friends order only cotton sweatshirts =\(\frac{1}{204}\)