In how many ways can we arrange the 13 letters of the word “COMMUNICATION” in which

(i} there are no restriction.

(ii) the word start with M and end with I.

(iii) the two letters C do not occur next to each other.

Guest Oct 13, 2017

#2**+2 **

Here's the third one :

Let's count the ways where the two C's * can* appear together

They can appear together in any one of twelve positions

And the number of identifiable arrangements of the other letters is

11 ! / [ 2! * 2! * 2! * 2! ]

So.....the total number of ways where they can occur together is

12 * 11! / [ 16] = 29,937,600

So.....the number of ways in which they don't appear together is

194,594,400 - 29,937,600 = 164,656,800

CPhill
Oct 13, 2017