Question

How many alphabet should there be in a language if one were to make 1 million distinct three digit initial using the alphabetical language ?
A.10
B.100
C. 56
D. 26

Answer 1

Hint: Firstly as per the given consider the information in the question, let the number of alphabets used be x at a time as in total three times it has to be used and in total 1 million numbers are formed so equating it to that and solving for x will yield our required answer.

Complete step-by-step answer:
As per the given, we should find that how many alphabet should be there in a language if one were to make 1 million distinct three digit
Let the alphabet used in the language be x
And in total we have to use three distinct alphabets in order to form one million words.
Digits with initial =3
Total number of initials =1000000
So,
 \[x.x.x = {10^6}\]
Now simplifying the above
 \[
  {x^3} = 1000000 \\
   \Rightarrow {x^3} = {10^6} \\
 \]
On taking cube root we get,
 \[
  x = {10^2} \\
   \Rightarrow x = 100 \\
 \]
Hence, option (b) is our correct answer.

Note: Various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
Permutations are the different ways in which a collection of items can be arranged. For example: The different ways in which the alphabets A, B and C can be grouped together, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. ... The same rule applies while solving any problem in Permutations.
Understand the question and form the equation properly and avoid mistakes while writing zeros, instead use the scientific notation to avoid such errors.