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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
- 6
- 8
- 9
- 7
Correct answer: 7
Solution
To find the smallest n for which 900 distinct n-digit numbers can be formed using the digits 2, 5, and 7, we calculate the total combinations as 3ⁿ. Setting 3ⁿ ≥ 900, we find that n must be at least 7, since 3⁶ = 729 (not sufficient) and 3⁷ = 2187 (sufficient). Thus, the smallest value of n is 7.
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