Find the number of different permutations of the letters of the word INDIA

  1. 20
  2. 40
  3. 50
  4. 60

Answer (Detailed Solution Below)

Option 4 : 60
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Detailed Solution

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Concept:

Let there be n objects, of which m objects are alike of one kind, and the remaining (n – m) objects are distinct. Then, the total number of permutations that can be formed from these objects is \(\rm \frac{n!}{m!}\)

 

Calculation:

The given word ‘INDIA‘ contains 5 letters, out of which two are alike of one kind (2 I‘s), and the other three letters are distinct.

∴Total number of their permutations = \(\rm \frac{5!}{2!}=\frac{5\times4\times3\times2\times1}{2\times1}=60\)

Hence, option (4) is correct. 

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