Permutation-Combination
Aptitude

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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

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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.


(1) Comment(s)


Arjit
 ()

Please explain the solution clearly.