SOLUTION: Find how many arrangements there are of the letters of the word GUMTREE if the G is somewhere to the left of the U and the M is somewhere to the right of the U.

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Question 1147180: Find how many arrangements there are of the letters of the word GUMTREE if the G is somewhere to the left of the U and the M is somewhere to the right of the U.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
There are 7 letters in GUMTREE, and the 2 E's are indistinguishable, so
there are 7!/2! = 2520 distinguishable arrangements total.  Exactly half of 
them, or 1260, have G somewhere left of U, (and the other half have G right of U).
In turn, by the same token, exactly half of those 1260, or 630, have M right 
of U.

Answer: 630 

Edwin