Question

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?

a. 91 divided by 15.
b. 77 divided by 255.
c. 1 divided by 204.
d. 1 divided by 15.

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)

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

Answer: c. 1 divided by 204.

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=(18!)/((18-4)!)=(18*17*16*15*14!)/(14!)=73440`

If the friends order only cotton sweatshirts, then the number of ways to order sweatshirts=
`^6P_4=(6!)/((6-4)!)=(6*5*4*3*2!)/(2!)=360`

Now, the probability that the friends order only cotton sweatshirts =
`(360)/(73440)=(1)/(204)`

Hence, the probability that the friends order only cotton sweatshirts =
`(1)/(204)`