Question 1112566: How many different words can be formed with the letters of the word "HAHA" Found 2 solutions by math_helper, Alan3354:Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!
When I see problems like this I like to first imagine all the letters are distinct, like WXYZ.
With WXYZ you can make 4! = 24 unique words.
Obviously this over-counts by a certain amount. How much does it over-count?
If WX is really HH then we've over-counted by 2! times (= the number of ways WX can be uniquely arranged).
If YZ is really AA then we've over-counted by another 2! times.
So the number of unique words with HAHA is 4!/(2!*2!) = 24/4 = .
Since this is a small number, the unique patterns can be easily enumerated:
AAHH, AHAH, AHHA, HAAH, HAHA, and HHAA
