Consider the sets S = {2, 3, 4, ..., 2n + 1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

A set of S consists of

i). All odd numbers from 1 to 55.

ii). All even numbers from 56 to 150.

What is the index of the highest power of 3 in the product of all the elements of the set S?

Set A = {2,3,4,5}

Set B = {4,5,6,7,8}

Two integers will be randomly selected from the sets above, one integer from Set A and one integer from Set B. What is the probability that the sum of the two integers will equal 9?