Using the digits

We need to find 3 digits even number using 1,2,3,4,5,6,7

So, units place can have 2,4,6

Number of even numbers if 2 is at unit place

As 2 is fixed next two places can be filled in ⁵P₂ ways

= 20

Similarly, if 4 will be at unit place, 3-digits number will be 20.

Also, if 6 will be at unit place, 3-digits number will be 20.

So, total 3-digits number will be 20+20+20 = 60