Question 667247
this falls under fractorial so each word can be arranged in how many ways you can use a ti-84 caculator or do by multiplication 
example

CAR is 3!  ! = factorial 
on t1-84 you enter 3 then MATH scroll over four places to PRB scroll down to 4:!
press enter answer 6 

or 
CAR= 3x2x1 

3x2= 6x1= 6 

CASTLE = 6!  SIX LETTERS SO ANSWER IS 720 
OR  6x5x4x3x2x1= 720