Lottery Related Question (Combinations and Probability)

Question

So if i have 8145,060 combinations to play out of a 6/45 lottery game,

how many possible combinations of 3 odds and 3 evens can i get, and what is the probability?

In this example, their answer was 2,727,340 combinations of 3 odd and 3 even, and a probability of 0.33484590659. How did they get those numbers?

The combination number was calculated using the formula ₄₅C_{6 .}

Answer 1

Kahlen,

In the first 45 whole numbers there are 22 even and 23 odd. Here we choose 3 out of 23 and 3 out of the 22

C(22,3)*C(23,3) = 2,727340

and the probability is 2,727340/8145,060 = 0.3348459