In one lottery game, contestants pick six numbers from 1 through 40 and have to match all six for
The big prize (in any order). What's the probability you'll win if you buy one ticket?

Question

Quizplus · Accepted Answer

There are a total of ${40\choose6}$ ways to pick six numbers out of 40. Therefore, the probability of winning if you buy one ticket is $\frac{1}{{40\choose6}}\approx 0.0000000228$, which is closest to option B. There are a total of 40 numbers and you need to pick 6, so the number of possible combinations is 40 choose 6, which is approximately 3.8 million. Since there is only one winning combination, the probability of winning with one ticket is 1 in 3.8 million, which is represented by option B.

In One Lottery Game, Contestants Pick Six Numbers from 1