Two different integers are to be selected from a set of 10 different integers in which half of the integers are even and half are odd. How many of the 45 possible selections consist of one even and one odd integer?

A) 5

B) 10

C) 20

D) 23

E) 25

Please give detailed and step-by-step explanation of your answer by showing all the computations and mathematical reasoning until the final answer.

Thanks