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(D) Each of the $n$ places in an $n$-digit number can be filled by any of the $3$ given digits ($2, 5$,or $7$).Since each place has $3$ choices,the to

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$7$

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(D) Each of the $n$ places in an $n$-digit number can be filled by any of the $3$ given digits ($2, 5$,or $7$).Since each place has $3$ choices,the total number of distinct $n$-digit numbers that can be formed is $3^n$.We are looking for the smallest integer $n$ such that $3^n \ge 900$.Calculating powers of $3$:$3^1 = 3$$3^2 = 9$$3^3 = 27$$3^4 = 81$$3^5 = 243$$3^6 = 729$$3^7 = 2187$Since $3^6 = 729  900$,the smallest value of $n$ for which at least $900$ distinct numbers can be formed is $7$.

$n$-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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