Expert: Jack Cheng - 11/11/2006

Question
how many different combinations are there to match every available outcome on the euro millions?
thanks

Answer
Hi Phil,

I am not very familiar with the Euro Millions, like how many number there are, or how many numbers are selected.  However, here's the general way to answer your question:

Let n be the total possible number of numbers that can be picked, and j be the number of numbers that you have to pick (what a mouthful to say). The formula for such combination is:

n! / (j!*(n-j)!)

(the n! means n*(n-1)*(n-2)*...*3*2*1, same with the j).

So let's say there are 40 numbers total, and you have to pick 8. The number of possible combinations is:

40! / (8!*(40-8)!) = 40!/(8!*32!)

Doing the factorial (n! and j!) on a calculator, I get 76,904,685 number of combinations. (If you are comfortable with factorials, you can also do canceling.)

You can find the combination on a calculator with n nCr j, where n and j are same as before and nCr is the key you have to press (or function to select in a graphing calculator).

I hope this helps,
Jack