Question

The number of $4$ digit odd numbers, that can be formed by using the digits $0,1,2,3,4,5,6$ when the repetition is allowed, is

• A. $120$
• B. $300$
• C. $420$
• D. $20$

Answer 1

The correct option is C

$420$

Explanation for correct option

The $4$ digit number is even.

Clearly the unit place will be $0,2,4,6$

But, the first digit cannot be $0$

When the unit place digit is $0$ we have $6\times 5\times 4=120$ number of choice

When the unit place digit is $2$ we have $5\times 5\times 4=100$ number of choice

When the unit place digit is $4$ we have $5\times 5\times 4=100$ number of choice

When the unit place digit is $6$ we have $5\times 5\times 4=100$ number of choice

Therefore total numbers of choice $=120+100+100+100=420$

Hence, the correct option is $\left(\mathrm{C}\right)$.