# Easy Permutation-Combination Solved QuestionAptitude Discussion

 Q. If $5 × {^nP_3} = 4 × {^{n+1}P_3}$ find $n$?
 ✖ A. 10 ✖ B. 12 ✖ C. 11 ✔ D. 14

Solution:
Option(D) is correct

${^nP_3} = n(n – 1) (n – 2)$

${^{n+1}P_3} = (n + 1) n (n – 1)$ [Replacing $n$ by $(n + 1)$]

⇒ $5 n(n −1)(n − 2) = 4(n +1)(n)(n −1)$

Divide both sides by $n (n-1)$

$5(n − 2) = 4(n +1)$

$5n −10 = 4n + 4$

$5n − 4n = 4 +10$

$n =14$

## (2) Comment(s)

Ashis
()

Why doesn't it work when I substitute the answer in the question?

Yoyo
()

Good work guys. keep it up.