I already submitted a wrong answer, but would like to know how others tackle it.?

A monkey sat in front of a special typewriter that only contained keys for the letters A, L, G, O, R, I, T, H, M, S. The monkey sat at the typewriter for a long time and pressed the keys. At the end of this time, the pattern typed on the page was quite remarkable. In fact, the monkey had typed out a large number of 10 letter words, all different mis-spellings of the word ALGORITHMS, one after another. Moreover, each mis-spelling had all of all the letters A, L, G, O, R, I, T, H, M, S and every letter was in the wrong position. If the monkey had typed every mis-spelling of this type exactly once, and had typed nothing other than these mis-spellings, how many times was the letter A typed in total?