Question

The numbers 1 through 20 printed on a lottery ticket. A player circles three numbers. At the official lottery drawing, balls with the numbers 1 through 20 are randomized in an urn. Three balls are drawn at random, one at a time without replacement. The player wins if the circled numbers match the three numbers drawn from the urn. What is the probability that the player wins?

Answer 1

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

P(the player wins) = 1/Number of possible winning number combinations

= 1/20C3

= 1/(20!/(3!x17!))

= 1/1140

= 0.00088