(D) Each of the $n$ places in the $n$-digit number can be filled in $3$ ways (using digits $2, 5,$ or $7$).Therefore,the total number of distinct $n$-

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(D) Each of the $n$ places in the $n$-digit number can be filled in $3$ ways (using digits $2, 5,$ or $7$).Therefore,the total number of distinct $n$-digit numbers that can be formed is $3^n$.We need to find the smallest integer $n$ such that $3^n \geq 900$.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 $3^6 = 729 < 900$ and $3^7 = 2187 \geq 900$,the smallest value of $n$ is $7$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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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:

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A
$6$
B
$8$
C
$9$
D
$7$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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