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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.
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! waysThe 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!= 1/189Thanks & RegardsBharat BajajaskIITians FacultyIIT Delhi
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