Problem
COM-B1-M01-P006 Even Three-Digit Numbers
#6
★★☆☆☆ Level 2 of 5
How many even three-digit numbers with distinct digits can be formed from \(0,1,2,3,4,5\)?
Split by the last digit: \(0,2,4\).
If the last digit is \(0\), the hundreds digit has \(5\) choices and the tens digit \(4\): \(20\). If the last digit is \(2\) or \(4\), the hundreds digit cannot be \(0\) or the last digit: \(4\) choices, then \(4\) for the tens digit. For two such cases: \(2\cdot4\cdot4=32\). Total: \(52\).
Good task on zero and casework.