Question

The number of all numbers having $5$ digits, with distinct digits is

• A. $99999$
• B. $9\times {}^9{P}_4$
• C. ${}^{10}{P}_5$
• D. ${}^9{P}_4$

Answer 1

The correct option is B $9\times {}^9{P}_4$

Total different digits are $0,1,2,3,4,5,6,7,8,9$
In a $5$ digit number, the first digit can not be filled with $0$
$\therefore$ Total different digits that can be formed
$=9\times 9\times 8\times 7\times 6=9\times \frac{9!}{(9-4)!}=9\times {}^9{P}_4$