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Nine hundred distinct n digit numbers are to be formed using o

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

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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

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

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 (n t im es) = 3^{n}

According to the question,

3^{n} \geq 900 \Rightarrow 3^{n - 2} \geq 100 \Rightarrow n - 2 \geq 5 \Rightarrow n \geq 7

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Question Text	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
Answer Type	Text solution:1
Upvotes	150