Question

in how many different ways can a police department arrange five suspects in a police lineup if each lineup contains all five people?
□ ways
(type a whole number.)

Explanation:

Step1: Determine the formula

This is a permutation problem of \(n\) distinct objects taken \(n\) at a time. The formula for permutations of \(n\) distinct objects is \(P(n,n)=\frac{n!}{(n - n)!}=n!\)

Step2: Calculate the factorial

Here \(n = 5\). The factorial of \(n\), denoted as \(n!\), is \(n\times(n - 1)\times\cdots\times1\). So \(5!=5\times4\times3\times2\times1\)

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Answer:

\(120\)