Question:
\(n\)-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of \(n\) for which 900 such distinct numbers can be formed, is :
\(n\)-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of \(n\) for which 900 such distinct numbers can be formed, is :
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Each of the n places can be filled in 3 ways, so there are \(3^n\) numbers; find the least n with \(3^n \ge 900\).
Updated On: Nov 11, 2026
- 6
- 7
- 8
- 9
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The Correct Option is B
Solution and Explanation
Each of the n places can be filled by any of the 3 digits, so the number of n-digit numbers is \(3^n\).
We need \(3^n \ge 900\).
\(3^6 = 729 < 900\) and \(3^7 = 2187 \ge 900\).
So the smallest n is 7.
Answer: (2) 7
We need \(3^n \ge 900\).
\(3^6 = 729 < 900\) and \(3^7 = 2187 \ge 900\).
So the smallest n is 7.
Answer: (2) 7
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