The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is \_\_\_\_\_\_\_\_\_\_\_\_\_\_.
Answer: 52
Solutions · 1
Official solution
Unit digit 0: remaining 2 digits chosen and arranged from the other 5: 5×4=20
Unit digit 4 or 6: hundreds digit can't be 0: for each such unit digit, hundreds digit has 4 choices (excluding 0 and the unit digit), tens digit has 4 remaining choices: 2×(4×4)=32
\[\text{Total} = 20+32 = 52\]