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Standard XI

Mathematics

Fundamental Principle of Counting

An n-digit nu...

Question

An n-digit number is a positive number with exactly n digits. 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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Solution

The correct option is B
7

Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive n-digit numbers are $3^{n}$ . Since we have to form 900 distinct numbers, hence $3^{n} \leq 900 \Rightarrow n$ = 7

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An n-digit number is a positive number with exactly n digits. 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

The correct option is B 7 Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive n-digit numbers are 3n. Since we have to form 900 distinct numbers, hence 3n≤900⇒n = 7

The correct option is B
7

Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive n-digit numbers are $3^{n}$ . Since we have to form 900 distinct numbers, hence $3^{n} \leq 900 \Rightarrow n$ = 7