Aptitude 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 $r = \textbf{4}$

**Vineela**

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

**ROHIT**

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

**Paras**

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

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