Problem 43 - Algebra and Trigonometry

Question

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?

Step-by-Step Solution

Answer

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

Step 1: Identify the type of problem

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

Step 2: 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.

Step 3: Substitute the values into the formula

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

Step 4: 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.