Aptitude Discussion

Q. |
If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in dictionary, then the word $SACHIN$ appears at serial number: |

✔ A. |
$601$ |

✖ B. |
$600$ |

✖ C. |
$603$ |

✖ D. |
$602$ |

**Solution:**

Option(**A**) is correct

If the word started with the letter $A$ then the remaining 5 positions can be filled in $5!$ Ways.

If it started with $C$ then the remaining 5 positions can be filled in $5!$ Ways

Similarly if it started with $H, I, N$ the remaining 5 positions can be filled in $5!$ Ways

If it started with $S$ then the remaining position can be filled with $A,C,H,I,N$ in alphabetical order as on dictionary

The required word $SACHIN$ can be obtained after the $5×5!=600$ Ways

i.e. $SACHIN$ is the $601^{th}$ letter.