Question

what is the value of the expression?
$_{6}p_{3}$
720
120
20
6

Explanation:

Step1: Recall permutation formula

The permutation formula is \(_{n}P_{r}=\frac{n!}{(n - r)!}\). Here \(n = 6\) and \(r=3\).

Step2: Substitute values into formula

\(_{6}P_{3}=\frac{6!}{(6 - 3)!}=\frac{6!}{3!}\).

Step3: Expand factorials

Since \(n!=n\times(n - 1)\times\cdots\times1\), then \(6! = 6\times5\times4\times3!\). So \(\frac{6!}{3!}=\frac{6\times5\times4\times3!}{3!}\).

Step4: Simplify the expression

Cancel out the \(3!\) terms. We get \(6\times5\times4=120\).

Answer:

120