Aptitude 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:

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

$= 5×4×3$

$=\textbf{60}$