By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 108

Topic: Probability

Q108

The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

  1. (a) 6/356/35
  2. (b) 3/353/35
  3. (c) 2/352/35
  4. (d) 1/351/35Correct answer

Solution.

Answer: (d) 1/351/35

  1. Treat Y as a consonant, as in the usual vowel-letter classification.
  2. There are four distinct consonants Z,L,G,Y and three identical O's.
  3. Alternation must be CVCVCVC.
  4. It has 4! arrangements, out of 7!/3! total distinct arrangements.
  5. Thus the probability is 24/840=1/35.