(B) Since each of the $n$ positions can be filled by any of the $3$ digits $(2, 5, 7)$,the total number of distinct $n$-digit numbers that can be form

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(B) Since each of the $n$ positions can be filled by any of the $3$ digits $(2, 5, 7)$,the total number of distinct $n$-digit numbers that can be formed is $3^n$.We are given that at least $900$ distinct numbers can be formed,so we have the inequality $3^n \geq 900$.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 minimum 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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Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

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

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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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Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

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