n-digit numbers are formed using only three digits 2, 5 and 7.

Question

$n$-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of $n$ for which 900 such distinct numbers can be formed, is:

Accepted Answer

In n digit number first place can be filled with any one of 2, 5, 7. So no of ways first digit can be filled  = 3

Similarly,

no of ways 2nd digit can be filled  = 3 ways

.

- - - - - - nth  - - - - - - - = 3 ways

$$ \therefore $$ Total numbers = 3 $$ \times $$ 3 $$ \times $$ 3 .... n times

= 3n

$$ \therefore $$ According to question, for smallest value of n,

3n > 900

36 = 729 < 900

37 = 2187 > 900

$$ \therefore $$ n = 7

Solutions · 1