Multiple choice

Different words being formed by arranging the letters of the word "INTERMEDIATE". All the words obtained are written in the form of a dictionary, The number of arrangements in which all vowels occur together.

  1. $43200$
  2. $21600$
  3. $151200$

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

The word INTERMEDIATE has 12 letters: I(2), N(1), T(2), E(3), R(1), M(1), D(1), A(1). Treating the vowels (I, I, E, E, E, A) as one block, we arrange 7 items (the block + 6 consonants) in 7!/2!2! ways, then arrange the vowels within the block in 6!/2!3! ways. The product is 151200.

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