If ^ 9 P_ r =3024, find the value of r. - Vidyadip

Question

If ${ }^{9} P_{r}=3024$, find the value of $r$.

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Answer

${ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}=\frac{n !}{(n-r) !}$
$ { }^9 \mathrm{P}_{\mathrm{r}}=\frac{9 !}{(9-r) !}$
$ \therefore 3024=\frac{362880}{(9-r) !}$
$ \therefore(9-r) !=\frac{362880}{3024}$
$ \therefore(9-r) !=120=5 !$
$ \therefore 9-\mathrm{r}=5$
$ \therefore \mathrm{r}=9-5=4$
Hence, $r=4$

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