CAT 2015 Quantitative Ability

Question : 33 of 34

Marks: +1, -0

If we arrange the letters of the word 'KAKA' in all possible ways, what is the probability that vowels will not be together in an arrangement?

Solution:

Letters of the word ‘KAKA‘ can be arranged in

(\;\;{4!}/{2!×2!})=6\;\text"ways"\;

If we consider the cases where vowels are together, then considering two A's as single entity, we have

(\;\;{3!}/{2!})=3

arrangements.
So. there must be (6 - 3) = 3 arrangements, where vowels are not together.
Therefore, the required probability =

3/6 = 1/2

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