Question

evaluate the expression.
$_{10}\text{p}_5$
(1 point)
○ 30,240
○ 5
○ 2
○ 252

Explanation:

Step1: Recall permutation formula

The formula for permutation is \(_{n}P_{r}=\frac{n!}{(n - r)!}\). Here \(n = 10\) and \(r=5\).

Step2: Substitute values into formula

\(_{10}P_{5}=\frac{10!}{(10 - 5)!}=\frac{10!}{5!}\).
Since \(n!=n\times(n - 1)\times\cdots\times1\), then \(10! = 10\times9\times8\times7\times6\times5!\).
So \(\frac{10!}{5!}=\frac{10\times9\times8\times7\times6\times5!}{5!}\).

Step3: Simplify the expression

Cancel out the \(5!\) terms. We get \(10\times9\times8\times7\times6\).
\(10\times9 = 90\), \(90\times8=720\), \(720\times7 = 5040\), \(5040\times6=30240\).

Answer:

\(30240\) (corresponding to the first option \(30,240\))