Question

How many different numbers of two digits can be formed with the digits $1,2,3,4,5,6$ no digits being repeated?

Answer 1

We have to fill up two places (since numbers are of two digits)
The first place can be filled up in $6$ ways, as any one of the six digits can be placed in the first place.

The $2^{nd}$ place can be filled up in $5$ ways as no digit is to be repeated.

Hence, both places can be filled up in $6\times 5=30$ ways.