How many ways can the letters of the word organism be arranged so the third letter is g?

So since the third place is fixed, we can count that out
organism has8 letters, count out the g since it is fixed
oranism has 7 letters
first slot=7 choices
2nd slot=6 choices (1 choice from 1 slot)
3rd=1 since only g can be here
4rd=5
5th=4
6th=3
7th=2
8th=1
so the answer is 7 times 6 times 1 times 5 times 4 times 3 times 2 times 1  (last one for g)=5040 ways

You can use a calculater and divide the minutes by the $$, hope that you