Question

$5$ digit number combinations.

Answer 1

A five digit number can be filled by ten digits $\left(0,1,2,3,4,5,6,7,8,9,\right)\mathrm{in}10$ways

Thus, each of the five places can be filled in $10$ ways.

$10\times 10\times 10\times 10\times 10=100000\mathrm{ways}$

Now, we need to exclude the possibility of $0$ existing at ten-thousand place

The number of $5$-digits numbers that have $0$ at ten-thousand place $10\times 10\times 10\times 10=10000\mathrm{ways}$

Therefore, the numbers of ways to write $5$-digits numbers $=100000-1000$

$=9000\mathrm{ways}$