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

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 [tex]{^59}C_5[/tex] ways

[tex]\frac{59!}{5!(59-5)!}[/tex]

[tex]\frac{59\times58\times57\times56\times55}{5\times4\times3\times2\times1}[/tex]

= 5,006,386 ways

Now, 1 red number from 1 through 35 can be selected in [tex]{^35}C_1[/tex] ways

[tex]\frac{35!}{1! (35-1)!}[/tex]

[tex]\frac{35}{1}[/tex]

= 35 ways

So, power ball ticket can be bought in = 5,006,386 [tex]\times[/tex] 35 = 175,223,510 ways