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Grade 12Algebra

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.

Samir Madan

12 Years agoGrade 12

1 Answer

bharat bajaj

Approved Tutor Answer12 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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