Find n, if: (17-n) ! (14-n) ! =5 ! - Vidyadip

Question

Find $n$, if: $\frac{(17-n) !}{(14-n) !}=5$ !

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Answer

$
\begin{aligned}
& \frac{(17-n) !}{(14-n) !}=5 ! \\
& \therefore \frac{(17-n)(16-n)(15-n)(14-n) !}{(14-n) !}=5 \times 4 \times 3 \times 2 \times 1 \\
& \therefore(17-\mathrm{n})(16-\mathrm{n})(15-\mathrm{n})=6 \times 5 \times 4
\end{aligned}
$
Comparing on both sides, we get
$
\begin{aligned}
& 17-n=6 \\
& \therefore \mathrm{n}=11
\end{aligned}
$

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