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Chapter 11: Problem 43

For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

Short Answer

Expert verified
The DJ can arrange the songs in 1,013,803,600 ways.

Step by step solution

01

Identify the type of problem

From the problem context, identify that this is a Permutations problem where order matters.
02

Set up the Permutations formula

The formula for a permutations problem is \(P(n, r) = \frac{n!}{(n-r)!}\) where 'n' is the total number of songs and 'r' is the number of songs to be selected.
03

Substitute the values into the formula

Substitute the values 'n = 13' and 'r = 7' into the permutations formula.
04

Calculate the Permutation

After substituting, the expression becomes \(P(13, 7) = \frac{13!}{(13-7)!} = \frac{13!}{6!}\). Use factorial calculation for both the numerator and the denominator to find the total number of ways the DJ can arrange the songs.

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