The artist, R. Locklen Jones, selects three paintings from a collection of six to display in a row. How many different arrangements of the display are possible?

20 zero

To find the number of different arrangements, we need to use the concept of permutations since the order of the paintings matters. We'll use the formula for permutations of n objects taken r at a time.

The formula for permutations is:
P(n, r) = n! / (n - r)!

In this case, n is the total number of paintings, which is 6, and r is the number of paintings selected to display in a row, which is 3.

Plugging the values into the formula, we get:
P(6, 3) = 6! / (6 - 3)!
= 6! / 3!

Calculating the factorials:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
3! = 3 x 2 x 1 = 6

Now, substituting the values into the formula:
P(6, 3) = 720 / 6
= 120

Therefore, there are 120 different arrangements possible for the display of three paintings selected from a collection of six.