Questions: For a segment of a radio show, a disc jockey can play 7 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged? ways

For a segment of a radio show, a disc jockey can play 7 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged?
ways

Transcript text: For a segment of a radio show, a disc jockey can play 7 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged? $\square$ ways Clear all Check answer

Solution

Solution Steps

Step 1: Understand the Problem

We are given a problem where a disc jockey can play $r$ records out of $n$ available records. We need to find out in how many ways the program for this segment can be arranged.

Step 2: Identify the Formula

The formula to calculate the permutations of $n$ items taken $r$ at a time is $P(n, r) = \frac{n!}{(n-r)!}$.

Step 3: Calculate Factorials

To solve this, we first calculate the factorial of $n$ which is $n! = 39916800$ and the factorial of $n-r$ which is $(n-r)! = 24$.

Step 4: Calculate Permutations

Using the formula, we calculate the permutations as $P(n, r) = \frac{n!}{(n-r)!} = 1663200$.