Question

Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's do not come together ?

Answer 1

Lets examine the possibility of i and s being together like is.

There are 10 characters in university and is can occupy the first two places, next two and so on in 9 ways.

When is occupies the first two places, the remaining 8 characters can occupy the remaining 8 places in 8! ways ( permutation). So the total possibilities fir i and s being together are 8!x9.

The total permutation for the 10 characters is 10!

So the possibilities of i and s not coming together is 10! - (8!x9)

Hence the probability of i and s not coming together in the word ‘university’ is

(10! - (8!x9))/10! = 1–1/10 = 90%.