Q57 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

If ${ }^{10} P_r=604800$ and ${ }^{10} C_r=120$ then $r=$

  • A
    $14$
  • Correct answer
    B
    $7$
  • C
    $8$
  • D
    $16$

Solution

We know that $10_{\mathrm{p}_{\mathrm{r}}}=10_{\mathrm{c}_{\mathrm{r}}} \cdot \mathrm{r} !$ $\Rightarrow 604800=120 . r ! \Rightarrow r !=5040$ $\mathrm{r} !=7 !=\mathrm{r}=7$

Hence, the correct answer is option: 'B'.

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