Question

Number of odd integers between $1000$ and $8000$ which have none of their digits repeated, is

• A. $1014$
• B. $810$
• C. $690$
• D. $1736$

Answer 1

Answer: (D)

$1736$

We have,

(1). For a number to be odd the unit digit should be either number $1,3,5,7,9$

(2). Thousand place can not be filled with $8$ or $9$.

The remaining two places can be filled in $=8\times 7=56$

So, the total number formed in this way

$=56\times 7$

$=392.......\left(1\right)$

$\therefore$ The remaining two places can be filled in $=8\times 7=56$

So, the total number formed in this way

$=56\times 6\times 4$

$=1344......\left(2\right)$

Then, total number are,

By equation (1)+(2) to and we get,

$392+1344$

$=1736$

Hence, this is the answer.