Problem
COM-B1-M04-P010 Paths of Length Two
#10
★★☆☆☆ Level 2 of 5
In the complete graph on \(6\) vertices, how many ordered paths \(A-B-C\) with distinct \(A,B,C\) are there?
Choose the middle vertex, then the two ends in order.
Choose the middle vertex \(B\) in \(6\) ways. Choose \(A\) in \(5\) ways and \(C\) in \(4\) ways. Total: \(6\cdot5\cdot4=120\).
Graph interpretation of ordered triples.