Question

What is the number of odd integers between $1000$ and $9999$ with no digit repeated?

• A. $2100$
• B. $2120$
• C. $2240$
• D. $3331$

Answer 1

The correct option is C $2240$

To form odd integers between $1000$ and $9999$ with no digits repeated.

So, the once place will only have odd digits.

So, once place can be filled in $5$ ways i.e. $1,3,5,7,9$.

Let there will be no $0$ in the integer, we have no. of integers

$6\times 7\times 8\times 5=1680$,

Let there will be $0$ in the hundred's place. We have no. of integers

$7\times 1\times 8\times 5=280$,

Let there will be $0$ in ten's place. We have no. of integers

$7\times 8\times 1\times 5=280$,

Total No. of integers $=1680+280+280=2240$

Hence, C is correct.