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

Question

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

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The number of $$n-digit$$ distinct numbers that can be formed using digits $$2$$, $$5$$ and $$7$$ is $$3n$$. We have to find n, so that $$3n$$≥$$900$$⇒ $$3n$$−$$2$$≥$$100$$ ⇒ n−$$2$$≥$$5$$ ⇒ n≥$$7Thus$$, the smallest value of n is $$7$$

An 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

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

An 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