Question

The number of four digit odd numbers that can be formed using $1,2,3,4,5,6,7,8,9$ (repetition of digits is allowed ) are

• A. $5\times 8^3$
• B. $5\times 9^2$
• C. $5\times 7^3$
• D. $5\times 9^3$

Answer 1

The correct option is D $5\times 9^3$

For a number to be odd, the units digit should be either of $1,3,5,7$ or $9$
$\therefore$ Total number of ways of choosing units digit $=5$

Since, it is given that the digit may be repeated. So, we have $9$ choices for ten's digit
Similarly, for rest two digits we can choose any of the $9$ digits

$\therefore$ No. of ways of choosing first and second digit is also $9$ for each.
$\therefore$ Total number of ways to form odd numbers is $5\times 9\times 9\times 9=5\times 9^3$.

Hence, the number of $4$ digit odd numbers can be formed is $5\times 9^3$.