Permutations

The number of ways you can change the order of a set of things is called the number of PERMUTATIONS of that set of things. For example, how many different ways can you arrange the letters in the word WHO? 

Answer: WHO    WOH    HWO    HOW    OHW    OWH = 6 ways
1      2      3      4      5      6
Each different letter arrangement is called a permutation of the word "WHO".

How about the word "STOP"? Well, here they are: 

   STOP     STPO     SOTP     SOTP     SPTO     SPOT   <- starts with "S"
   TSOP     TSPO     TOSP     TOPS     TPSO     TPOS   <- starts with "T"
   OSTP     OSPT     OTSP     OTPS     OPST     OPTS   <- starts with "O"
   PSTO     PSOT     PTSO     PTOS     POST     POTS   <- starts with "P"
There are 24 ways to order the letters in "STOP". Is there a general rule here? Fortunately, yes. Here's the rule for "STOP":
  1. There are 4 ways to pick the first letter.
  2. After you pick the first letter there are 3 ways to pick the second letter.
  3. After you pick the first 2 letters, there are 2 ways to pick the third letter.
  4. After picking the first 3 letters, there is only 1 letter left to pick.
So the number of ways to order the letters in "STOP" is 4 x 3 x 2 x 1 = 24 ways!

So, here is a problem for you:

I am playing Scrabble and I have 5 letters on my tray.
How many ways can I order the letters on my tray? ______________