For a segment of a radio​ show, a disc jockey can play 5 records. If there are 7 records to select​ from, in how many ways can the program for this segment be​ arranged?

Answer 1

This is a permutation problem (order matters) because the order in which the records are played is important.

The number of ways to arrange 5 records out of 7 is given by the formula for permutations:

P(7, 5) = 7! / (7 - 5)! = 7! / 2!

P(7, 5) = 7 * 6 * 5 * 4 * 3 = 2520

Therefore, there are 2520 ways the program for this segment can be arranged.