If you need to find thea) Find all distinct permutations of the word "MATHSARMCANMOL".numberof permutations, then see this Wikipedia article.

The same as the number of permutations of "MATHSARCANOL".b) How many permutations are there that has three consecutive M- MMM?

You can form a required permutation in two steps: first form a permutation of "ATHSARCANOL" and then insert 3 M's. There are 11 letters in "ATHSARCANOL", so there are 12 places where the three M's can be inserted. Use the Rule of Product to find the total number possibilities for the two steps.c) How many permutations are there without adjacent Ms?