Virtual Gate

Question

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?

Comments

the path starts at u and ends at w. So there is only 1 place to place v that is between u and w

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I am taking vertex set as $V = \{1,2,3,4,5,6,7,8,9,10\}$.

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13700 possible if each vertex is labelled

Answer 1

is it 60621?

Answer 2

13700 possible if each vertex is labelled