Multiple choice

The probability that all the vowels of the word EAMCET come together, when the letters are arranged at random is

  1. $\displaystyle \frac{1}{5}$
  2. $\displaystyle \frac{1}{6}$
  3. $\displaystyle \frac{1}{7}$
  4. $\displaystyle \frac{1}{8}$
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A Correct answer
Explanation

Word EAMCET has 6 letters: E, A, M, C, E, T. Vowels are E, A, E. Treat (EAE) as one unit. Total units = 4 (EAE, M, C, T). Arrangements = 4! * (3!/2!) = 24 * 3 = 72. Total arrangements = 6!/2! = 360. Probability = 72/360 = 1/5.

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