Question

When you buy a Powerball ticket, you select 5 different white numbers from among the numbers 1 through 59 (order of selection does not matter), and one red number from among the numbers 1 through 35. How many different Powerball tickets can you buy

Answer 1

175,223,510 tickets

Explanation:

To buy a Powerball ticket,

White number tickets are ranging from 1 through 59. Also, the order of the selection does not matter as given in the question and red number tickets from among the numbers 1 thorugh 35. So, this a case of selection.

If we want to select 5 different white numbers from 1 through 59, it can be done in
`{^59}C_5` ways

`(59!)/(5!(59-5)!)`

`(59*58*57*56*55)/(5*4*3*2*1)`

= 5,006,386 ways

Now, 1 red number from 1 through 35 can be selected in
`{^35}C_1` ways

`(35!)/(1! (35-1)!)`

`(35)/(1)`

= 35 ways

So, power ball ticket can be bought in = 5,006,386
`*` 35 = 175,223,510 ways