Question

7. In a lottery, players must match five numbers plus a bonus number. Five white balls are chosen from 59 white balls numbered from 1 to 59, and one red ball (the bonus number)

is chosen from 35 red balls numbered 1 to 35. How many different results are possible?

Answer 1

There are 175,223,510 ways.

Explanation:

If the order of the white balls doesnt metter, we have as many possibilities to pick white balls as ways of pick 5 elements from a set of 59. That number is the combinatorial number of 59 with 5 given by

`{59 \choose 5} = (59!)/((59-5)!5!) = 5,006,386`

We have 35 different ways to pick the red ball. Combining both events, we have

35*5,006,386 = 175,223,510

ways of picking the 5 numbers and the bonus one.