Question

Use the formula for n Pr to evaluate the following expression.5P0

Answer 1

The expression given is,

`^5P_0`

We are to use the formula below

`\begin{gathered} \mathrm{The\: number\: of\: possibilities\: for\: choosing\: an\: ordered\: set\: of\: r\: objects\: } \\ \mathrm{from\: a\: total\: of\: n\: objects}\text{.} \\ nPr=(n!)/(\left(n-r\right)!) \end{gathered}`

Therefore,

`\begin{gathered} \mathrm{Plug\: in}\: n=5,\: r=0 \\ (5!)/(\left(5-0\right)!)=(5!)/(5!)=1 \\ \therefore^5P_0=1 \end{gathered}`

Hence, the answer is 1.