+0

probability

0
360
2

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

(i}      there are no restriction.

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

Oct 13, 2017

#1
+98196
+2

Here's the first one

C - O - M - M - U - N - I  - C - A -  T - I - O - N

The number of  "identifiable" arrangements is given by :

13!  /  [ 2! * 2!  * 2!  * 2! * 2!  ]  =

13!  [ 32]  =  194,594,400  "words"

Oct 13, 2017
edited by CPhill  Oct 13, 2017
edited by CPhill  Oct 13, 2017
#2
+98196
+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

Oct 13, 2017
edited by CPhill  Oct 13, 2017