Urgent maths questions plz help.

1) If I had ten possible smilies :mog: :moggie: :choc: :moomba:, and I had ten places to fill them with, what would be the total number of arrangements I could have? Would that be 10!/4! ?

2) How do I do log to the base 2 of something on the calculator?

3) What is Boltzmans constant?

Any help would be greatly appreciated. :smash:

1) 10!, I'd imagine, but it's been so long since I did permutations and stuff that I'm probably wrong.
2) log_n x = (log₁₀ x) / (log₁₀ n).
3) http://en.wikipedia.org/wiki/Boltzmann's_constant

Permutations:
n P k = n!/((n-k)!)

So 10 P 10 = 10!

10!/4! would be if you have 10 smilies and only 6 slots to fill.

That's if you can't use twice the same smilie.

Argh crap I should have said 4 different smilies with 10 places to fill them with (they can be used more than once). What would that be then?

Thanks for your help.

I think that would just be 4¹⁰ = 1,048,576. You mean you have four symbols, 10 slots, right?

Yep that's what I meant, thanks heaps. :beer: