In how many ways can three letters (not necessarily distinct from one another) be selected from the letters of the word PARALLELOGRAMS ?

The word PARALLELOGRAMS contains the letters P, E, O, G, M, S once, the letter R twice, and the letters A and L thrice.

We can choose 3 letters in the following ways:

1. All 3 letters are distinct. Number of such ways = $$9_{C_3=\ 84}\ $$
2. 1 letter is repeated twice. Number of such ways = $$3_{C_1\ \times\ }8_{C_1\ =\ 24}\ $$
3. 1 letter is repeated thrice.Number of such ways = $$2_{C_1=\ 2}\ $$

Thus, the total number of ways = 84 + 24 + 2 = 110