Question

The number of natural numbers less than $7,000$ which can be formed by using the digits $0,1,3,7,9$ (repetition of digits allowed) is equal to :

• A. $372$
• B. $375$
• C. $374$
• D. $250$

Answer 1

The correct option is C $374$

Natural numbers less than $7,000$, means first number can not be greater than $6$.
There are four positions to fill.


$\therefore$ There are $3$ ways to fill the first position and there are $5$ ways to fill the remaining positions.
Hence, required number
$=3\times 5\times 5\times 5-1(\because 0000\text{is not included})$
$=374$