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If ""^nPr=720 and ""^nCr=120 , find n...

If `""^nP_r=720` and `""^nC_r=120` , find `n`

Text Solution

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The correct Answer is:
`""^nPr=(n!)/((n-r)!);""^(n)C_(r)=(n!)/(r!(n-r)!)`
`=>(""^nP_(r))/(r!)=""^nC_(r)`
(i.e)`(720)/(r!)`=120 `=>(720)/(120)`=r!
r!=6=3!`=>`r=3
`^nP_(3)`=720
n(n-1)(n-2)=720=`10xx9xx8=>`n=10
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