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?

a. 1/52
b. 9/455
c. 44/7
d. 1/35

Answer 1

The probability that all four friends order cotton sweatshirts from among 16 colors, with 7 being cotton, is calculated based on permutations of the 7 cotton options.

Step-by-step explanation:

To calculate the probability that the four friends order only cotton sweatshirts, we must consider the total number of cotton sweatshirt options and the total possibility of selections they can make. Since there are 16 colors of sweatshirts and only 7 are all cotton, the friends have a pool of 7 cotton colors to choose from. However, each friend orders a different color without repeats which is a condition for permutations. The total number of ways to select 4 different-colored sweatshirts from 7 is 7P4 which means the calculation is 7!/(7-4)! or 7 x 6 x 5 x 4.