Aptitude Discussion

Q. |
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language? |

✔ A. |
100 |

✖ B. |
50 |

✖ C. |
26 |

✖ D. |
1000 |

**Solution:**

Option(**A**) is correct

1 million distinct 3 digit initials are needed.

Let the number of required alphabets in the language be $n$.

Therefore, using $n$ alphabets we can form $n × n × n = n^3$ distinct 3 digit initials.

**Note**: Distinct initials are different from initials where the digits are different.

For instance, $AAA$ and $BBB$ are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.

This $n^3$ different initials $= 1$ million

i.e. $n^3 = 10^6$ (1 million $= 10^6$)

⇒ $n^3 = (10^2)^3$

⇒ $n = 10^2 = 100$

Hence, the language needs to have a minimum of $100$ alphabets to achieve the objective.

**Arjit**

*()
*

Please explain the solution clearly.