Any 1 of the 100 can be chosen first
Next.....we can choose any 1 of the other (100 - 2) = 98 ( we can't choose the other one from the first state)
Next.....we can choose any of the remaining (100 - 4) = 96 (we have chosen two from two states and we can't choose the remaining two from either state)...so...we only have 96 to choose from
Continuing with this pattern :
Then.... one from the remaining (100 - 6) = 94
Then... one from the remaining (100 - 8) = 92
So
100 * 98 * 96 * 94 * 92 = 8,136,038,400 ways !!!
THIS IS INCORRECT !!!