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We want to count step-by-step paths between points of the form (x, y) in coordinates Only two kinds of stens are allowed: a right-sten which increm

We want to count step-by-step paths between points of the form (x, y) in coordinates Only two kinds of stens are allowed: a right-sten which increm

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We want to count step-by-step paths between points of the form (x, y) in the plane with integer coordinates. Only two kinds of steps 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 (10, 10) that go through (5, 5)? Express your answer as an integer. The WolframAlpha calculator e accepts factorial !, combinations C(n, k), and permutations P(n, k) notation to help you produce an integer value based on the course formulas.
Transcribed Image Text:We want to count step-by-step paths between points of the form (x, y) in the plane with integer coordinates. Only two kinds of steps 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 (10, 10) that go through (5, 5)? Express your answer as an integer. The WolframAlpha calculator e accepts factorial !, combinations C(n, k), and permutations P(n, k) notation to help you produce an integer value based on the course formulas.
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