How many ways the word 'EQUATION' can be arranged so that all the vowels will always come together?

  1. 5!
  2. 4!
  3. 4 × 5!
  4. 4! × 5!

Answer (Detailed Solution Below)

Option 4 : 4! × 5!
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NDA 01/2025: English Subject Test
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Detailed Solution

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Concept:

n objects can be arranged in n! ways

When two or more objects are taken together they are considered as one object.

Calculation:

The total number of vowels in EQUATION is 5 (E, U, A, I, O)

So, we can consider them as single unity and they can arrange themselves in 5! ways.

Rest 3 consonants along with the vowels together can arrange in 4! ways.

So, the total number of ways the word can be arranged = 4! × 5!

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