G, D, I, I, F form strings such as GDIIF OR DGIFI, how many strings there are if there is at least one letter between the two I's?
The number of combinations using all the letters given = 5!/2! (2! for the repeating I's)
Subtract this from the combinations where I's appear together.
To get this, consider the 2 I's together to be a single letter. That way we have only 4 characters.
These can be arranged in 4! ways. In 4! combinations, the 2 I's appear together.
So, answer = 5!/2! - 4! = 60 - 24 = 36.