Answer:
30,240
Step-by-step 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:
[tex]^{n}P_{r}=\frac{n!}{(n-r)!}[/tex]
Here, n = 10 and r = 5
Using the values, we get:
[tex]^{10}P_{5}=\frac{10!}{(10-5)!}\\\\ ^{10}P_{5}=30240[/tex]
This means, the program of the segment can be arranged in 30,240 different ways.
