Find n if: ^6 P_2=n ^6 C_2 - Vidyadip

Question

Find n if: ${ }^6 \mathrm{P}_2=\mathrm{n}{ }^6 \mathrm{C}_2$

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Answer

$
\begin{array}{ll}
& { }^6 \mathrm{P}_2=\mathrm{n}\left({ }^6 \mathrm{C}_2\right) \\
\therefore \quad & \frac{6 !}{(6-2) !}=\mathrm{n} \frac{6 !}{2 !(6-2) !} \\
\therefore \quad & \frac{6 !}{4 !}=\mathrm{n} \frac{6 !}{2 ! 4 !} \\
\therefore \quad & \mathrm{n}=2 !=2 \times 1=2
\end{array}
$

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