Counting numbers without repeated digits

A multi-digit number cannot begin with zero. Parity is controlled by its units digit. Each supplied digit is used at most once. Write the positions, such as;;;. Fill a restricted units or leading position first so that every later factor counts the digits actually remaining. If zero is available, split even numbers into units digit zero and units digit nonzero even. These cases cannot overlap and together cover all even numbers. From digits 0,1,2,3,4, three-digit even numbers ending in zero number 4 x 3=12. Ending in 2 or 4 gives 2 x 3 x 3=18. Total: 30. Check: after a nonzero units digit is used, zero is still forbidden in the first position but allowed in an interior position. A fixed-length code may start with zero only when stated.