A word game player has four tiles with the letters A, N, P, and S.

1. How many arrangements of these letters are possible? Why?

   Answer (a):

   $4! = 24$

2. Draw a tree diagram that shows all of the possible arrangements and explain how a decision chart relates to the tree diagram.

   Hint (b):

   There are four decisions to make, but not every decision has the same number of available choices to pick from.

3. What is the probability of a two-year-old randomly making a word using these four letters?

   Hint (c):

   Those tiles can be used to spell PANS, NAPS, SNAP and SPAN.