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NDA 2 2024 Maths, question 14

Topic: Algebra

Q14

In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

  1. (a) 33
  2. (b) 66Correct answer
  3. (c) 99
  4. (d) 1212

Solution.

Answer: (b) 66

  1. The vowels I,I,A fill positions 1,3,5 in 3!/2!=3 distinct ways.
  2. N and D fill positions 2,4 in 2!=2 ways.
  3. The product is 3×2=6; the repeated I must not be counted twice.