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

(b) : Distinct n digit numbers which can be formed using digits 2,5 and 7 are 3^n. \ n should be such that \ 3^n >= 900 => 3^n-2 >= 100 or n-2 >= 5 or n >= 7 Hence the least value of n is 7

An (n)-digit number is a positive number with exactly (... | Permutations and Combinations (Mathematics)

(b) : Distinct $n$ digit numbers which can be formed using digits 2,5 and 7 are $3^n$ . $\\ n$ should be such that $\\ 3^n \geq 900 \Rightarrow 3^{n-2} \geq 100 \text { or } n-2 \geq 5 \text { or } n \geq 7 \\$ Hence the least value of $n$ is 7

Explanation

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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