SOLUTION: Find how many arrangements there are of the letters of the word GUMTREE if the M is somewhere to the left of both Es and the U is somewhere between them.

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Question 1147179: Find how many arrangements there are of the letters of the word GUMTREE if the M is somewhere to the left of both Es and the U is somewhere between them.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The M,E,U,E must appear in that order going left to right.
We must now insert the G, T, and R somewhere in these 5 blanks, 

_____M_____E_____U_____E_____

So there are 5 places to put the G.

Regardless of which of the 5 blanks we put the G in, there
will be 6 places to put the T.  To demonstrate that, suppose
we put the G between the U and the second E.  And we see,
there are now 6 places to put the T.  And it wouldn't matter
which of the blanks we had put the G in, it would still add 
one more blank to put the T in.

_____M_____E_____U__G__E_____

By the same token, when we put the T in one of those 6 blanks,
it will add one more blank, and there will be 7 places to put 
the R.
 
Answer: 5∙6∙7 = 210

Edwin