Question

Substitute values into the formula for npr.14!n Pr=( 14 - 7)!(Type an integer or a decimal.)There can beways to listen to the 7 songs.

Answer 1

We have the formula npr, this formula has some values and a factory term

$_nP_r=\frac{14!}{(14-7)!}$

First, we solve the subtraction and then the factorial terms

$\begin{gathered} _nP_r=\frac{14!}{7!} \\ _nP_r=\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12\cdot13\cdot14}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7} \end{gathered}$

we can cancel some terms

$\begin{gathered} _nP_r=8\cdot9\cdot10\cdot11\cdot12\cdot13\cdot14 \\ _nP_r=17297280 \end{gathered}$

The answer is 17297280