Question

how many three letter words can be formed by the word letter EQUATION

Answer 1

In the word EQUATION there are 8 different letters.

We have 8 variants to choose the first letter, 8 variants to choose the second letter and 8 variants to choose the third letter. All the variants compatible with each other, so, as a result, we have $8\cdot8\cdot8 = 512$  different words.