Powerball q

[kyro]

I feel dumb. I'm assuming I'm just missing something obvious. In Powerball, you pick 5 numbers ranging from 1-53 and one "Powerball" ranging from 1-42. If you get them all right, you win. Shouldn't the odds of winning be 1 in 53*52*51*50*49*42 ~ 14,463,212,400?

According to their website, it's 1 in 120,526,770.00 (http://powerball.com/powerball/pb_prizes.asp)

[Slade]

You dont have to choose the first five numbers in order so you're 120 times more likely to win.

[Luzion]

[ QUOTE ]
I feel dumb. I'm assuming I'm just missing something obvious. In Powerball, you pick 5 numbers ranging from 1-53 and one "Powerball" ranging from 1-42. If you get them all right, you win. Shouldn't the odds of winning be 1 in 53*52*51*50*49*42 ~ 14,463,212,400?

According to their website, it's 1 in 120,526,770.00 (http://powerball.com/powerball/pb_prizes.asp)

[/ QUOTE ]

Dont use permutations. Use combinational probability since order does not matter.

C(53,5) * 42 = 120,526,770

which is (53!/5!48!) * 42
or simplied [ (53*52*51*50*49)/(5*4*3*2) ] * 42

= 120,526,770

This is assuming the Powerball number can be a duplicate of one of the regular 5 I believe.

[kyro]

[ QUOTE ]
You dont have to choose the first five numbers in order so you're 120 times more likely to win.

[/ QUOTE ]

well duh. like i said, probably just missing something obvious. good thing i'm not looking to make a career out of something probability-related like being an actuary.

aw crap.