Question

Nine hundred distinct $n$ digit numbers are to be formed using only the three digits $2,5$ and $7$. the smallest value of $n$ for which this is possible is

• A. $4$
• B. $8$
• C. $7$
• D. $9$

Answer 1

Answer: (C)

$7$

Using 2,5 and 7 with repetition, each place of n digits number can be chosen in 3 ways. So total of n digit number is equal to $=3\times 3\times 3\times ....\times 3\left(ntimes\right)=3^n$

According to the question, $3^n\ge 900\Rightarrow 3^{n-2}\ge 100\Rightarrow n-2\ge 5\Rightarrow n\ge 7$