Arrangements of the word $ABCDEFGGGG$ If we consider the word $ABCDEFGGGG$. To find the number of arrangments for that word, we just calculate: $\frac{10!}{4!}$.
But if now we want to find the total number of arrangements for that word such that $2$ $G$'s must come together and the two other $G$'s be separated. One of the arrangements is for example: $ABGGCDGEFG$.
*Note that the two G's that are separated must also be separated from the other 2'G that are together.
How can we think about this problem?
Any help will be very appreciated.  

the answer is not $75600$. The reason is some of the combinations are repeated. 
For example $G G GG$ are separated but when we permute them the first and the second $G$ will make the same combination. So, the solution is $2! * 7C3 * 6!$ .
