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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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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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