How many $3$ digit even numbers can be formed by using digits $1,2,3,4,5,6,7$, if no digits are repeated?
There are three places to be filled in _ _ _ I wrote it like this
_ _ $2$
_ _ $4$
_ _ $6$
Now each of the two blanks can be filled in $P(6,2)$ ways. So adding results of three cases i have $3$. $P(6,2)$ which gives me $90$ ways. But the textbook states $60$ ways. Can someone suggest how ?