Cecilia,

Suppose all 9 letters are distinguishable, perhaps by colour. Assume there is a red, blue and green copy of each letter. Since you now have 9 distinct letters there are 9! permutations of these letters. Here for example are three of them.

What happens if the Gs are no longer distinct? Suppose they are all black then the 3 permutations above become

The three permutations are now indistinguishable. In fact for every arrangement of the Hs and Ss, for example

there are 3! ways to place the 3 Gs. Hence if the 3 Gs are indistinguishable then there are only 9!/3! permutations.

What happens now if the Hs are all black?

Penny