1. In how many ways can four letters of the word ‘SERIES’ be arranged?
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By: anil on 05 May 2019 02.40 am
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.
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