For an art exhibit, Craig has to choose 3 ceramic mugs out of the 7 that he made over the summer. In how many ways can he arrange these 3 mugs in a row?

7P3 = 210

To find the number of ways Craig can arrange the 3 ceramic mugs in a row, we will use the concept of permutations.

A permutation is an arrangement of objects where the order matters. In this case, we want to find the number of ways Craig can arrange the 3 mugs, so the order in which the mugs are arranged matters.

To solve this problem, we can use the formula for permutations. The formula for finding the number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n - r)!

Where "!" denotes the factorial function.

In this case, Craig has 7 mugs and he wants to select 3 mugs. So we need to find P(7, 3).

P(7, 3) = 7! / (7 - 3)!
= 7! / 4!

Simplifying further:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
4! = 4 x 3 x 2 x 1 = 24

Plugging the values into the formula:

P(7, 3) = 5040 / 24
= 210

Therefore, there are 210 ways Craig can arrange the 3 ceramic mugs in a row.