Factorial Fun

Every once in a while I'll see something in my math homework that forces my brain into a traffic jam.  I know I've seen that exclamation point used in math before, but I haven't the slightest idea anymore what it means.  Time to brush up on Factorials:

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

Oh yeah!  I recognize that descending series of multiplication problems.  I think I had a calculator that saved me some longhand work in high school when we went over factorials.  The calculator helped me rip through my homework, but didn't help me remember the content of the lesson.

Another important detail to remember about Factorials:  0! = 1.  This is often described as one of these weird things you just have to accept.  I tried to read up on and understand completely why, but I'm now comfortable sticking to the old stand-bye answer of:  it just does.  For a more thorough explanation follow this link!


When I teach factorials and permutations I'll use problems like this one about license plates:


License plates for cars have to be unique. If a license plate contains 6 characters consisting of 2 letters followed by 4 digits example:  QW2354, 

• how many different license are possible?
  
  
  

  [26] x [26] x [10] x [10] x [10] x [10] = 6,760,000 

• how many different license are possible if letters were allowed to repeated but numbers are not allowed to be repeated?
  
  
  

  [26] + [26] + [10] + [9] + [8] + [7] = 3,407,040