Question

Six-digit odd numbers, greater than $6,00,000$ that can be formed using the digits $5,6,7,8,9$ and $0$ if repetition of digits is allowed is

• A. $6^6$
• B. $11664$
• C. $15552$
• D. $4\times 6^5$

Answer 1

The correct option is C $15552$

We have $6$ digits, $5,6,7,8,9$ and $0$ and we have to form odd numbers greater than $6,00,000.$

The unit's place can only be filled by $5,7$ or $9$ since we have to form odd numbers.
$\therefore$ The unit place can be filled in $3$ ways.

The first place (lakh's position) can be occupied by the digits greater than or equal to $6$. Therefore, the lakh's position can be filled in $4$ ways.

Each of the remaining $4$ places can be filled by any of the $6$ digits in $6^4$ ways.

Hence, the total number will be $4\times 6\times 6\times 6\times 6\times 3=15552$