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Classrooms A has capacity of 25 seats. Ax denotes the number of possib

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Bunuel
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Classrooms A has capacity of 25 seats. Ax denotes the number of possib [#permalink] New post   17 Feb 2021, 08:00
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Classrooms A has capacity of 25 seats. \(A_x\) denotes the number of possible seating arrangements of room ‘A’, when 25 of ‘x’ students are to be seated in this room in a row. If \(A_n – A_{n–1} = 25!(49C25)\) then what is the value of ‘n’?

(A) 51
(B) 50
(C) 49
(D) 48
(E) 47


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adityashinde88
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Re: Classrooms A has capacity of 25 seats. Ax denotes the number of possib [#permalink] New post   19 Oct 2023, 23:36
Hey Bunuel Sir, can you share the solution as well..
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Re: Classrooms A has capacity of 25 seats. Ax denotes the number of possib [#permalink] New post   20 Oct 2023, 23:32
please sir, can i get the solution of this? I am not understanding the question clearly
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Classrooms A has capacity of 25 seats. Ax denotes the number of possib [#permalink] New post   21 Oct 2023, 03:34
Given: Classrooms A has capacity of 25 seats. \(A_x\) denotes the number of possible seating arrangements of room ‘A’, when 25 of ‘x’ students are to be seated in this room in a row.
Asked: If \(A_n – A_{n–1} = 25!(49C25)\) then what is the value of ‘n’?

\(A_x = ^xC_{25}*25!\)
\(A_n - A_{n-1} = 25! (^nC_{25} - ^{n-1}C_{25}) = 25!^{49}C_{25}\)
\(^nC_{25} - ^{n-1}C_{25} = \frac{n!}{25!(n-25)!} - \frac{(n-1)!}{25!(n-26)!} =\frac{ n!-(n-1)!(n-25)}{25!(n-25)! }= \frac{(n-1)! (n-(n-25))}{25!(n-25)!} = \frac{(n-1)!}{24!(n-1-24)!} = ^{n-1}C_{24} = ^{49}C_{25}\)

If n=50;
\(^{49}C_{24} = ^{49}C_{25}\)

IMO B
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Classrooms A has capacity of 25 seats. Ax denotes the number of possib [#permalink]
21 Oct 2023, 03:34
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