Telephone Numbers without repeated digits In a city with telephone numbers with $6$ digits,how many telephone numbers exist without repeated digits?What does this mean? That my telephone number shouldn't have twice the same number or that my telephone number and yours should not have the same digits?

It means that each telephone number consists of 6 distinct digits. You need to find all such telephone numbers.

For example, $125432$ isn't a valid telephone number because $2$ appears twice, however, $125430$ is valid.

Assuming that $0$ cannot be the first digit, the number of distinct telephone numbers would be:

$$ 9.9.8.7.6.5 = \frac{9.9!}{4!} $$