AP ICET 2016 Paper

Question : 143 of 200

Marks: +1, -0

If the letters of the word WISDOM are permuted at random, then the probability that the vowels do not come together is

Solution:

WISDOM has 2 vowels
Let us first arrange the 4 consonants which can be done in 4! ways

Now, the 2 vowels can occupy the 5 places (marked by rectangular boxes). Itcan be done in

^5P_2=20

ways.
Total 6 letters of WISDOM can be arranged in 6! ways.
∴ Required probability

={4!×^5P_2}/6!=20/{6×5}=2/3

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