No repetition of digits

We can choose any of the $6$ digits for the units’ place; then, any one of the five remaining digits for the tens’ place; then, any one of the four remaining digits for the hundreds’ place. Hence, by the Principle: “If one event can occur in $h$ ways and if, after its occurence or at the same time, a second event can occur in $k$ ways, then the two events can occur in the stated fashion in $(h)(k)$ ways”, we can form $(4)(5)(6) = 120$ different numbers.