Please do the followings question (Discrete Math about Combinatorics) (pls no plagiarism)

Ql Prove the following identity by giving a combinatorial argument: (illitlill'ii') We want to count step-by-step paths between points in the plane with integer coordinates. Only two kinds of step are allowed: a right-step which increments the x coordinate, and an up-step with increments the y coordinate. How many paths are there from (0,0) to (20,30) that do not go through either of the points (10,10) or (15,20)? 03 Suppose 2n + 1 numbers are selected from {1,2, 3, . . . ,4n}. Using the Pigeonhole Principle, show that for any positive integer j that divides 2n, there must be two selected numbers whose difference is j. Clearly indicate what are the pigeons, holes, and rules for assigning a pigeon to a hole