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Permutations and Combinations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Permutations and Combinations (p-2)1 Mark
Question
Find $x$ if ${ }^n P_r=x^n C_r$
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Answer

$
\begin{aligned}
& { }^n \mathrm{P}_{\mathrm{r}}=x\left({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}\right) \\
& x=\frac{{ }^n \mathrm{P}_{\mathrm{r}}}{{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}} \\
& =\frac{\frac{\mathrm{n} !}{(\mathrm{n}-\mathrm{r}) !}}{\frac{\mathrm{n} !}{(\mathrm{n}-\mathrm{r} !) \mathrm{r} !}} \\
& =\mathrm{r} !
\end{aligned}
$

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