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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 n, if: $\frac{(15-n) !}{(13-n) !}=12$
✓

Answer

$
\begin{aligned}
& \frac{(15-n) !}{(13-n) !}=12 \\
& \therefore \frac{(15-\mathbf{n})(14-\mathbf{n})(13-\mathbf{n}) !}{(13-\mathbf{n}) !}=12 \\
& \therefore(15-\mathrm{n})(14-\mathrm{n})=4 \times 3
\end{aligned}
$
Comparing on both sides, we get
$
\begin{aligned}
& 15-n=4 \\
& \therefore n=11
\end{aligned}
$

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