Let the nine different letters ` A, B, C… I in {1, 2, 3, …, 9}`. Then find the probability that product `(A - 1)(B - 1) … (I - 9)` is an even number.

Answer

1

Explanation

Given set of number is {1, 2, ……, 9} in which 4 are even and 5 are odd, so in the given product it is not possible to arrange to substract only even number from odd number, there must be at least one factor involving substraction of an odd number from another odd number. So at least one of the factor is even. Hence, product is always even.
`therefore` Required probability = 1