There are 7 items on a shelf. How many distinct ways can the items be arranged?

Question

There are 7 items on a shelf. How many distinct ways can the items be arranged? 

 

There are 12 horses in a race. How many ways can the horses finish first, second and third? 

Answer 1

If all seven items on a shelf are distinguishable, then 7! (seven factorial) different arrangements are possible; this equals the product of all integers from 7 down through 1.

 

outcomes of the horse race: 12C3 possibilities; = 12! divided by [9! 3!]  

 

I trust that you know what factorials are.