Question

For a segment of a radio show a disc jockey can play 5 records. If there are 10 to select from in how many ways can’t he program for this segment be arranged

Answer 1

30,240

Explanation:

Total number of records = 10

Number of records to select = 5

We have to arrange 5 records out of 10 for the segment. The order in which the records are selected matters so this is a problem of permutations. So we have to find the number of permutations of 10 songs taken 5 at a time. The formula for permutations is:

`^(n)P_(r)=(n!)/((n-r)!)`

Here, n = 10 and r = 5

Using the values, we get:

`^(10)P_(5)=(10!)/((10-5)!)\\\\ ^(10)P_(5)=30240`

This means, the program of the segment can be arranged in 30,240 different ways.