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Help please:
Find the number of different ways in which the 9 letters of the word GREENGAGE can be arranged if exactly two of the Gs are next to each other.
The answer is 5040.. but I'm confused because there's 3 Gs and I don't know how to find the # of ways where 2 Gs are separated from the other one.
Simply 'choose' 2 Gs out of 3, and the remaining 7 letters can be completely random!
G G _ _ _ _ _ _ _...............[consider GG to be 'attached' together so that it can alternate in 2! ways]
n = 2! x 3c2 x 7!.................. [but don't forget that there are 3 recurring Es too!]
..............3!
...= 5040...... Q.E.D