Multiple choice

The letters of the word 'HEXAGON' are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangement is

  1. $1680$
  2. $840$
  3. $420$
  4. $\dfrac { 8! }{ 2! } $
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B Correct answer
AI explanation

The word HEXAGON contains 7 distinct letters, giving a total of 7 factorial, or 5040, possible arrangements. The word has 3 vowels (E, A, O), and if their specific order is not considered, we must divide by the number of ways they can be arranged. Dividing the total arrangements by 3 factorial gives 5040 divided by 6, which equals 840.

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