Question

How many $5$ digit numbers can be formed from the digits $0,1,3,7,9$ without repeatition?

• A. $48$
• B. $96$
• C. $120$
• D. $256$

Answer 1

The correct option is B $96$

Given digits: $0,1,3,7,9$

First place can be filled by $4$ ways: $1,3,7$ or $9$

Second place can be filled by $4$ ways: any remaining $4$ numbers

Third place can be filled by $3$ ways: any remaining $3$ numbers

Fourth place can be filled by $2$ ways: any remaining $2$ numbers

Fifth place can be filled by $1$ ways: last remaining number


$\therefore$ Total number of $5$ digits number $=4\times 4\times 3\times 2\times 1$
$=4\times 4!$
$=96$