In how many ways can four letters of the word ‘SERIES’ be arranged?

We can see that letters are S, S, E, E, I, R.

Case 1: When all 4 letters are different. There is only one way where we select one each S, E, I, R.

Total number of 4 letter words which can be formed using these letters = $$4!$$ = 24.

Case 2: When all 2 letters are of 1 type and 2 letters are different.

Total number of ways in which 4 letter can be chosen = 2C1*3C2 = 6

Total number of 4 letter words which can be formed using these letters = $$6*\dfrac{4!}{2!}$$ = 72

Case 3: When all 2 letters are of 1 type and remaining 2 letters are of different another same type. There is only one way when we select S, S, E, E.

Total number of 4 letter words which can be formed using these letters = $$\dfrac{4!}{2!*2!}$$ = 6

We have considered all possible cases. Hence, total number of four letters of the word can be made = 24 + 72 + 6 = 102. Hence, option D is the correct answer.