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Retired Moderator
Joined: 16 Apr 2020
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What is the value of r?
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22 Jul 2021, 03:39
22 Jul 2021, 03:39
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Question Stats:
62% (03:09) correct
37% (02:16) wrong based on 8 sessions
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If \(\frac{^{22}P_{r+1}}{^{20}P_{r+2}} = \frac{11}{52}\), then what is the value of \(r\)?
Show: ::
7
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: What is the value of r?
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26 Jul 2021, 06:44
26 Jul 2021, 06:44
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KarunMendiratta wrote:
If \(\frac{^{22}P_{r+1}}{^{20}P_{r+2}} = \frac{11}{52}\), then what is the value of \(r\)?
Show: ::
7
Explanation:
\(\frac{^{22}P_{r+1}}{^{20}P_{r+2}} = \frac{11}{52}\)
\(\frac{(22)!}{(22-r-1)!}\frac{(20-r-2)!}{20!} = \frac{11}{52}\)
\(\frac{(22)(21)(20)!}{(21-r)(20-r)(19-r)(18-r)!}\frac{(18-r)!}{20!} = \frac{11}{52}\)
\(\frac{(22)(21)}{(21-r)(20-r)(19-r)} = \frac{11}{52}\)
\((21-r)(20-r)(19-r) = \frac{(52)(22)(21)}{11} = (52)(2)(21) = (14)(13)(12)\)
On comparison, \((21-r) = 14\) or \((20-r) = 13\) or \((19-r) = 12\)
Therefore, \(r= 7\)
Re: What is the value of r?
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23 Jul 2024, 13:18
23 Jul 2024, 13:18
Expert Reply
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