Find the number of all possible ways of placing 8 different books on a shelf.

It is also     

That is, there are 8 different objects.  In how many ways can you select 8 and order them.

32 positions

idea: divide the shelf in 8 imaginary slots.
you can place the first book in one of 8 slots, that's 8 possiblities.

now one slot is occupied, so the shelf has only 7 remaining slots. the second book can now be placed in one of 7 slots, that's 7 possiblities.

and so on..

the last book can only be placed in excactly one remaining slot, that's 1 possibility.
total possibilities = 8*7*6*5*4*3*2*1 = 8! (factorial) = 40320