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PART - 1 CH - 6 Permutations and Combinations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPART - 1 CH - 6 Permutations and Combinations1 Mark
Question
Prove that :
${ }^n P_n=6 .{ }^n P_{n-3}$
✓

Answer


$\begin{aligned} \text { LHS }= & { }^n P _n=\frac{n!}{(n-n)!}=\frac{n!}{0!}=n! \\ \text { RHS }= & 6 \cdot{ }^n P _{n-3}=6 \times \frac{n!}{(n-n+3)!}=\frac{6 n!}{3!} \\ & =\frac{6 n!}{6}=n!\end{aligned}$
$\quad\quad$LHS $=$ RHS$\quad$Hence proved.

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