Expert: Sherman D. - 11/13/2006

Question
Euro Millions, on the ticket it advises there is a 1 in 76,275,360 chance of winning the jackpot.
It draws 5 numbers from 1 - 50.
It draws 2 numbers from 1 - 9.

How can this be. I thought the way to work it out was
50(1) x 49(2) x 48(3) x 47(4) x 46(5) = 254,251,200 / 5 = 50,850,240 possible combinations

then you add
9(1) x 8(2) = 72 / 2 (as there are only 2 possible outcomes) = 36 possible combination

which is 50,850,240 + 36 = 50,850,276 combinations

So where do they get 76,275,360 chances from?

Answer
Here is how you do it

(50/1)(49/2)(48/3)(47/4)(46/5) = 2118760
(9/1)(8/2) = 36

2118760 * 36 = 76275360

You almost had it.

Did you see or understand where you went wrong.

This would be the combination formula to use

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

50C5 = (50!)/(5!(50 - 5)!)
50C5 = (50!)/(5! * 45!)
50C5 = 2118760

9C2 = (9!)/(2!(9 - 2)!)
9C2 = (9!)/(2 * 7!)
9C2 = 36

Multiply them together and you get 76,275,360