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

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