Is it $720?$

The Gateway to Computer Science Excellence

0 votes

A complete graph on n vertices is an undirected graph in which every pair of distinct vertices is connected by an edge. A simple path in a graph is one in which no vertex is repeated. Let G be a complete graph on 10 vertices. Let u, v, w be three distinct vertices in G. How many simple paths are there from u to v going through w?

+4

no of vertices total_paths

3 1

4 7C1 * 2!

5 7C2 * 3!

6 7C3 *4!

7 7C4 * 5!

8 7C5 * 6!

9 7C6 * 7!

10 7C7 * 8!

final answer would be summing up all these values

3 1

4 7C1 * 2!

5 7C2 * 3!

6 7C3 *4!

7 7C4 * 5!

8 7C5 * 6!

9 7C6 * 7!

10 7C7 * 8!

final answer would be summing up all these values

52,345 questions

60,487 answers

201,823 comments

95,294 users