How many k-vertex paths does the graph $K_{{n1},{n2}}$ have?

Question

$K_{{n1},{n2}}$ is a bipartite graph.

For the graph $K_{n}$ with k-vertex it has $$\frac{n(n-1)(n-2)...(n-k+1)}{2}$$ graphs, but what about $K_{{n1},{n2}}$??

Answer 1

Hints: If $k$ is even, the path starts on one side of the bipartition and ends on the other. If $k$ is odd, the path starts and ends on the same side of the bipartition.