Question

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

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

Answer 1

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

$\square$ $\square$ $\square$ $\square$

6 7 8 5

5 odd numbers

Last place can be filled in 5 ways.

Remaining 3 place can be filled

by remaining 8 numbers in ${}^8{P}_3$ ways.

Thus, total possibility ${=}^8{P}_3\times 5$

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

= 1680 ways. / numbers.