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A 9 digit number formed using only the digits 1,2,3.............,9 without repetition, then the probability that difference of the digits at equal distances from the beginning and the end respectively is always one is.

A 9 digit number formed using only the digits 1,2,3.............,9 without repetition, then the probability that difference of the digits at equal distances from the beginning and the end respectively is always one is.

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago
There are 4 even and 5 odd numbers. Therefore the middle digit is odd.
Hence, this middle digit can be selected in 5 possible ways.
4 pairs of numbers in which the difference of numbers in each pair is 1 can be arranged in 4! ways
The numbers in each pair can be rearranged leading to 2^4 such rearrangements.
Total count of numbers = 9!

Therefore the probability
= 5 x 4! x 2^4/9!
= 1/189

Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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