Question

The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. A ticket is defined as a set of five white and 1 red number.

Answer 1

The question continues ; I take it is defined as a set of five white and one red number how many possible different Powerball tickets can be purchased how many possible different winning Powerball tickets are there

Explanation:

he concept of combinatorics ( combination and permutation) is applied her

nPr = n!/(n-r)!

nCr = n!/(n-r)!r!

Hence number of possible different powerball tickets = number of ways of selection

= selecting 5 white ball from a total of 69 and selecting a red ball from a total of 26

= 69C5 x 26C1

using the formula above for combination

= 69!/(69-5)!5! x 26!/(26-1)!1!

= 292, 201, 338 ways