SOLUTION: Find the number of ways of arranging the letters of the word CALENDAR in such a way that exactly 2 letters are present between L and D.

Algebra ->  Permutations -> SOLUTION: Find the number of ways of arranging the letters of the word CALENDAR in such a way that exactly 2 letters are present between L and D.      Log On


   



Question 892689: Find the number of ways of arranging the letters of the word CALENDAR in such a way that exactly 2 letters are present between L and D.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
L _ _ D _ _ _ _
_ L _ _ D _ _ _
_ _ L _ _ D _ _
_ _ _ L _ _ D _
_ _ _ _ L _ _ D
D _ _ L _ _ _ _
_ D _ _ L _ _ _
_ _ D _ _ L _ _
_ _ _ D _ _ L _
_ _ _ _ D _ _ L




For each of those 10 ways above to have exactly 2 letters between the letters 
L and D, the blanks can be filled with all distinguishable arrangements of the
6 letters CAENAR, which has 2 indistinguishable A's.  The number of
distinguishable arrangements of CAENAR is 6%21%2F2%21

So the final answer is: 10%2A%286%21%2F2%21%29%22%22=%22%223600

Edwin