Multiple choice

The letters of the word $'CLIFTON'$ are arranged randomly in a row. What is the chance that two vowels come together?

  1. $\dfrac {2}{7}$
  2. $\dfrac {1}{7}$
  3. $\dfrac {5}{7}$
  4. $\dfrac {3}{7}$
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A Correct answer
Explanation

Total letters = 7 (C, L, I, F, T, O, N). Vowels are I, O. Treating (IO) as one unit, we have 6 units to arrange in 6! ways. The vowels can be arranged in 2! ways. Total arrangements = 7!. Probability = (6! * 2!) / 7! = 2/7.

AI explanation

The word CLIFTON has 7 letters, including 2 vowels (I, O) and 5 consonants. To find the probability of the two vowels coming together, we use the probability formula of favorable outcomes divided by total outcomes. The total arrangements of the word are 7! = 5040; treating the two vowels as a single unit gives 6! arrangements for the units, multiplied by 2! for the internal arrangement of the vowels, yielding 720 x 2 = 1440 favorable outcomes. The probability is 1440 divided by 5040, which simplifies to 2/7.

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