Permutation-Combination
Aptitude

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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

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

$= 5×4×3$

$=\textbf{60}$


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