probability

Question

0

1559

2

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

CPhill · Answer 1 · 2017-10-13T05:04:35

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"

CPhill · Answer 2 · 2017-10-13T05:54:45

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