Question

If the letters of the word ASSASSINATION are arranged at random. Find the Probability that

(a) Four S’s come consecutively in the word
(b) Two I’s and two N’s come together
(c) All A’s are not coming together
(d) No two A’s are coming together.

Answer 1

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