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NDA 2016 Maths · Mathematics · Permutations and Combinations · medium

The number of arrangements of the letters of the word ROUTE in which all the vowels are together is

Single correct option

The number of arrangements of the letters of the word ROUTE in which all the vowels are together is
  1. A. 3636
  2. B. 7272
  3. C. 2424
  4. D. 1212
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Answer: (A) 3636

Treat the three vowels O, U, E as one block. The block and the consonants R and T make 3 objects, arranged in 3!=63!=6 ways. The vowels can be permuted inside the block in 3!=63!=6 ways. Hence the total is 6×6=366\times6=36. Forgetting the internal arrangement gives 6, and 5!=1205!=120 ignores the condition.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake