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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
If ${ }^n P_r=1814400$ and ${ }^n C_r=45$, find $r$.
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Answer

$
\begin{array}{ll}
& { }^n \mathrm{P}_{\mathrm{r}}=1814400,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=45 \\
\therefore \quad & \frac{{ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}}{{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}}=\frac{1814400}{45} \\
\therefore \quad & \frac{\mathrm{n} !}{(\mathrm{n}-\mathrm{r}) !} \times \frac{\mathrm{r} !(\mathrm{n}-\mathrm{r}) !}{\mathrm{n} !}=\frac{1814400}{45} \\
\therefore \mathrm{r} != & 40320 \\
\therefore \mathrm{r} != & 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\
\therefore \mathrm{r} != & 8 ! \\
\therefore \mathrm{r}= & 8
\end{array}
$

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