Permutation-Combination
Aptitude

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Q.

If $5 × {^nP_3} = 4 × {^{n+1}P_3}$ find $n$?

 A.

10

 B.

12

 C.

11

 D.

14

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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.