Question

for a segment of a radio show, a disc jockey can play 6 records. if there are 8 records to select from, in how many ways can the program for this segment be arranged?
ways

Explanation:

Step1: Identify the permutation formula

The number of permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 8\) (total records) and \(r=6\) (records to play).

Step2: Calculate factorial values

\(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1\) and \((n - r)!=(8 - 6)!=2!=2\times1\)

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Answer:

\(20160\)