I walk past this great big billboard on my way to college every morning. At the moment, a McDonalds advert is up:

"The McDonalds New McChoice Menu. <8 pictures of fries, drink, big mac etc>. Only 99p each. In 40312 combinations."


This really bugs me. I got thinking about it: How can 8 items be arranged in 40312 ways? I assume the following could be valid combinations:
drink, fries, mcslurry
drink, fries, bigmac
drink
drink, fries
etc etc

If I were to work out the number of combinations I would do:
8C1 + 8C2 + 8C3 + ... + 8C8

But this doesn't equal 40312. Oh no. So, I played around with some numbers. The closest I can get is that they have (mistakenly) done something with 8P8, which equals 40320. This is, funnily enough, 8 more than the claimed combinations.

However, if they're using permutations they they count:
drink, fries and
fries, drink
as 2 different choices!!