Hi,
Mary has 'seven' decorative vases to arrange on a shelf.
How many different arrangements are possible? 7! = 7*6*5*4*3*2*1 = 5040(calculator)
Probability is much like every discipline in Mathematics (Algebra, for
example, has operations or formulas that work best in particular situations
or 'types of problems', as you put it so well)
n! operation works with these types.