Question

Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 56 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 23. find the probability of winning the jackpot.

Answer 1

Because the drawings are independent, the probability is the product of the probabilities of winning each drawing:
1/C(56, 3) × 1/23 = 1/(27,720×23) = 1/637,560

_____
C(n, k) = n!/(k!(n-k)!)
C(56, 3) = 56*55*54/(3*2*1) = 56*55*9