Permutation-Combination
Aptitude

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Q.

If ${^6P_r} = 360$ and ${^6C_r} = 15$ find $r$?

 A.

$3$

 B.

$4$

 C.

$5$

 D.

$6$

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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
 ()

answer is 4(option :B)plzz correct the answer


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 $r!$ Smile



Paras
 ()

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