Multiple choice

One word is chosen randomly from total word that could be made by using letters of the word "VARANSI". Find the probability that it would start with a vowel?

  1. $\frac{9}{49}$
  2. $\frac{1}{840}$
  3. $\frac{3}{7}$
  4. $\frac{12}{23}$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word VARANSI has 7 letters with A and I repeated (2 vowels, 5 consonants). Total distinct arrangements = 7!/(2!) = 2520. Words starting with vowel: Choose first letter (A or I) = 2 choices, arrange remaining 6 letters with one repeated vowel = 6!/2! = 360. Probability = (2 × 360)/2520 = 720/2520 = 3/7.

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