5. A lattice path from (x0, y0) to in the ay plane is defined as a sequence of points (x0, y0), (x1,y1), , such that each and each, ± 1,i =1,2, n - 1. How many lattices paths are there from (0,1) to (10,3)? How many of them do not touch or cross the t axis?

4. Let G be a simple graph. A path of G is a sequence of distinct vertices v0,v1, Uh such that and are adjacent for each i = 1,2,..., k. The length of the path v0, v1 , ..., is k. The degree of a vertex is the number of edges incident to that vertex. Show that if the minimum degree of G is greater than or equal to k, then G has a path whose length is at least k.

5. A lattice path from (x₀, y₀) to in the ay plane is defined as a sequence of points (x₀, y₀), (x₁,y₁), , such that each and each, ± 1,i =1,2, n - 1. How many lattices paths are there from (0,1) to (10,3)? How many of them do not touch or cross the t axis?

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