Powerball:
Choose 5 numbers from 1 to 59 with no replacement and order is not important, + choose 1 number from a seperate 1 to 35.
C(n,r)= n!/(r! * (n-r)!)
There are C(59,5) ways to pick the first 5 numbers or 5006386 ways.
There are C(35,1) ways to pick the Powerball or 35 ways.
So 5006386*35 = 175,223,510 possible Powerball numbers.