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InterviewSolution
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The letters of the word ‘SOCIETY’ are placed at random in a row. What is the probability that three vowels come together ? |
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Answer» There are 7 letters in the word SOCIETY. ∴ Total number of ways of arranging all the 7 letters = n(S) = 7!. When the case of three vowels being together is taken, then the three vowels are considered as one unit, so the number of ways in which 5 letters (SCTY–4, IEO–1) can be arranged = 5! Also the 3 vowels can be arranged amongst themselves in 3! ways ∴ Total number of favourable cases = 5! × 3! ∴ Required probability = \(\frac{5!\times3!}{7!}\) = \(\frac{1}{7}\) |
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