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Two classrooms A and B having capacity of 25 and (n-25) Seats respectively. `A_n`, denotes the number of possible seating arrangements of room 'A', when 'n' students are to be seated in the rooms, starting from room 'A', which is to be filled up full to its capacity If `A_n-A_(n-1)=25!(C(49,25))` then the value of 'n' is

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`A_n=nC_25*25!`
`A_(n-1)=(n-1)C_25*25!`
`A_n-A_(n-1)=25!*.^49C_25`
`.^nC_25*25!-.^(n-1)C_25*25! =.^49C_25*25!`
`.^nC_25-.^(n-1)C_25=.^49C_25`
`.^nC_r+.^nC_(r-1)=.^(n+1)C_25`
`.^(n-1)C_24=.^nC_25-.^(n-1)C_25`
`.^(n-1)C_24=.^nC_25-.^(n-1)C_25`
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