# Easy Permutation-Combination Solved QuestionAptitude Discussion

 Q. If ${^6P_r} = 360$ and ${^6C_r} = 15$ find $r$?
 ✖ A. $3$ ✔ B. $4$ ✖ C. $5$ ✖ D. $6$

Solution:
Option(B) is correct

${^nP_r} = {^nC_r} × r!$

${^6P_r} = {^6C_r} × r!$

$360 = 15 × r!$

$r! = \dfrac{360}{15}$

$= 24$

$= 4 × 3 × 2 × 1$

⇒ $r! = 4!$

Therefore $r = \textbf{4}$

## (4) Comment(s)

Vineela
()

Deepak
()

Thank you for notifying the error. It was typo. Corrected it.

ROHIT
()

$^nP_r=^nC_r\times r!$, it means first we are selecting by using $^nC_r$ and then we are arranging those selected things by using $r!$

Paras
()

please explain, $^nP_r=^nC_r\times r!$