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  • An - digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers a

An \mathrm{n} - digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only three digits 2,5 and 7 .The smallest value of n for which this is possible is

Option: 1

6


Option: 2

7


Option: 3

8


Option: 4

9


Answers (1)

best_answer

The number of n-digit distinct numbers that can be formed using digits 2,5 and 7 is 3^{n}.  We have to find n. so that 3^{n} \geq 900

\mathrm{\Rightarrow \quad 3^{n-2} \geq 100 \Rightarrow n-2 \geq 5 \quad \Rightarrow \quad n \geq 7}.

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Sayak

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