# What is the probability that you pick the winning numbers of lottery?

A state runs a lottery called “Pick 6.” A player buys a lottery ticket showing 6 of the numbers from 1 through 40. Then a set of 6 numbers is chosen as the winning numbers, and anyone whose ticket matches those numbers wins a prize. (The order of the numbers does not matter.)

I know the answer is 1 over 40C6. Could you briefly explain how to get this solution?

## 1 Answer

There are $$N={40\choose 6}$$ different combinations of numbers possible in the lottery, and the player chooses one of them. The probability of choosing the correct one is $$1/N$$.