Given word is ASSASSINATION
Total number of letters in ASSASSINATION is 13
In word ASSASSINATION, there are 3A’s, 4S’s, 2I’s, 1T’s and 1O’s
Total number of ways these letters can be arranged
(a) Four S’s come consecutively in the word
If 4S’s come consecutively then word ASSASSINATION become.
So, now numbers of letters is 1 + 9 = 10
(b) Two I’s and two N’s come together
So, now numbers of letters is 1 + 9 = 10
(c) All A’s are not coming together
Firstly, we find the probability that all A’s are coming together
If all A’s are coming together then
So, now numbers of letters is 1 + 10 = 11
Now, P(all A’s does not come together)
= 1 – P(all A’s come together)
(d) No two A’s are coming together
First we arrange the alphabets except A’s
There are 11 vacant places between these alphabets.
Total A’s in the word ASSASSINATION are 3
∴ 3 A’s can be placed in 11 place in 11C3 ways
∴ Total number of words when no two A’s together
