How many different words can be formed with the letters of the word 'INDIA'?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60
The number of arrangements of \(n\) letters in which one letter occurs \(p\) times is \(\frac{n!}{p!}\), because swapping the identical letters gives no new word. INDIA has 5 letters, with I occurring twice.
Words \(\displaystyle=\frac{5!}{2!}=\frac{120}{2}=60\)