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

The answer is "0.00088"

Explanation:

Many ways of selecting r articles of n,
`\to ^nC_r = (n!)/((r! * (n-r)!))`

P(wins the player) =
`\frac{1}{\text{Any combinations of possible numbers}}`

`= (1)/(^(20) C_3)\\\\`

`= (1)/((20!)/((3!* 17!)))\\\\= (1)/(1140)\\\\= 0.00088`