Count the total number of permutations of the word "calculus": there are 8 letters, hence 8! = 40,320 total permutations.
Count the number of permutations in which the two L's occur next to each other. Effectively we're now talking about words consisting of 7 letters, of which there are 7! = 5,040.
It follows that there are
8! - 7! = 35,280
words in which two L's do not appear next to each other.
