How many letters should the alphabet of a language contain to form 1 million…
2023
How many letters should the alphabet of a language contain to form 1 million different three-letter initials?
Answer: A. 100 — Let the language contain n letters. A three-letter initial can be formed in n × n × n = n^3 ways if repetition is allowed. Given: n^3 = 1,000,000 = 10^6. So,…
- A.
100
- B.
1000
- C.
10
- D.
120
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Correct answer: A
Let the language contain n letters. A three-letter initial can be formed in n × n × n = n^3 ways if repetition is allowed.
Given: n^3 = 1,000,000 = 10^6.
So, n = cube root of 10^6 = 10^2 = 100.
Therefore, the language needs 100 letters.
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