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If ${ }^{10} P_r=604800$ and ${ }^{10} C_r=120$ then $r=$
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Verified Answer
The correct answer is:
$7$
We know that
$10_{\mathrm{p}_{\mathrm{r}}}=10_{\mathrm{c}_{\mathrm{r}}} \cdot \mathrm{r} !$
$\Rightarrow 604800=120 . r ! \Rightarrow r !=5040$
$\mathrm{r} !=7 !=\mathrm{r}=7$
$10_{\mathrm{p}_{\mathrm{r}}}=10_{\mathrm{c}_{\mathrm{r}}} \cdot \mathrm{r} !$
$\Rightarrow 604800=120 . r ! \Rightarrow r !=5040$
$\mathrm{r} !=7 !=\mathrm{r}=7$
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