Question

The number of four digit odd numbers with all distinct digits that can be formed using $1,2,3,4,5,6,7,8,9$ is

• A. $4\times {}^{8}P{}_3$
• B. $5\times {}^{8}P{}_3$
• C. $4\times {}^{7}P{}_3$
• D. $5\times {}^{7}P{}_3$

Answer 1

The correct option is B $5\times {}^{8}P{}_3$

Even numbers = 2,4,6,8
Odd numbers = 1,3,5,7,9
$\to$ In order for a number to be odd, only the last digit has to be odd.
So, the no. of ways are ;

8

7

6

5

(Starts (only odd numbers)
with 9-1)
= $5\times$ ${}^8{P}_3$