Question

If $5{\times }^n{P}_3=4{\times }^{n+1}{P}_3,$ then $n=?$

• A. $10$
• B. $11$
• C. $12$
• D. $14$

Answer 1

The correct option is D $14$

$\frac{n!}{(n-3)!}\times \frac{(n+1)!}{(n-2)!}=\frac{4}{5}$

$⟹\frac{n-2}{n+1}=\frac{4}{5}$

$n=14$