# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. How many different five-letter words can be formed using the letter from the world $APPLE$?
 ✖ A. 120 ✔ B. 60 ✖ C. 240 ✖ D. 24

Solution:
Option(B) is correct

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:
$\Rightarrow \dfrac{5!}{2!}$

$= 5×4×3$

$=\textbf{60}$