Question

How many distinguishable ways can the letters of the word COMMUNICATION  be arranged in order?

Answer 1

The word can be arranged in n! ways where n is the number of letter in the word which is 13.

Now as we are asked to find distinguishable formations ,so we have to see that the two M's ,O's,I's, are taken care of properly, for example , COMUNICATIONM and COMUNICATIONM will be treated as the same word. To achieve this we will divide n! by (number of occurrence of the letter )! . So all the three letters M,O,I occurs 2 times.Therefore we will divide n! by (2! * 2! *2!).

Answer is 13!/(2! *2! *2!)