How many different five-letter words can be formed using the letter from the world APPLE?

Answer: Option B

If the two P’s were distinct (they could have different subscripts and colours), the number of possible permutations would have been 5! = 120

For example let us consider one permutation: P₁LEAP₂

Now if we permute the P’s amongst them we still get the same word PLEAP. The two P’s can be permuted amongst them in 2! ways.

We were counting P₁LEAP₂ and P₂LEAP₁ as different arrangements only because we were artificially distinguishing between the two P’s Hence the number of different five letter words that can be formed is:
= $$\frac{5!}{\left(1!\right)\left(2!\right)\left(1!\right)\left(1!\right)}$$
= 60