How many $3-$digit even numbers can be formed using the digits $1,3,4,6,8$ and $9$ without any digit being repeated?

Total no.of digits $=6$

no.of even digits $=3$

for no.to be even last digit

should be even $\therefore$ last

place can be filled in '3'

ways. As repetition is

not allowed hence no. of

ways of filled $1^{st}$ & $2^{nd}$

Place is '5' & '4'

$\Rightarrow 543$

$\therefore$ Total Ways $=5\times 4\times 3=60$