Permutation and Combination  Quant/Math  CAT 2016
Question 4 the day:
July 17, 2002
The question for the day is from the topic permutation and combination. Permutation and Combination is one area which if you are reasonably comfortable, you will be able to answer questions in minimum time.
Question:
 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?
(1) 26
(2) 50
(3) 100
(4) 1000
Correct Answer  (3)
Solution:
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 is 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.
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