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Consider the following identity: n 2 2n Σ (1)² - (²). = k=0 (1) Perhaps it seems mysterious? But if you try a few small values of n, you may begin to suspect it is correct. (a) Suppose n€ N and that we have a set S of cardinality 2n containing n distinct objects, all coloured red, and n distinct objects, all coloured blue. Let k = Z satisfy 0 < k < n. How many ways are there to sample n objects from S, subject to k of them being red? Briefly justify your answer.

Consider the following identity: n 2 2n Σ (1)² - (²). = k=0 (1) Perhaps it seems mysterious? But if you try a few small values of n, you may begin to suspect it is correct. (a) Suppose n€ N and that we have a set S of cardinality 2n containing n distinct objects, all coloured red, and n distinct objects, all coloured blue. Let k = Z satisfy 0 < k < n. How many ways are there to sample n objects from S, subject to k of them being red? Briefly justify your answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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Consider the following identity: n 2 2n Σ (1)² - (²). = k=0 (1) Perhaps it seems mysterious? But if you try a few small values of n, you may begin to suspect it is correct. (a) Suppose n€ N and that we have a set S of cardinality 2n containing n distinct objects, all coloured red, and n distinct objects, all coloured blue. Let k = Z satisfy 0 < k < n. How many ways are there to sample n objects from S, subject to k of them being red? Briefly justify your answer.
Transcribed Image Text:Consider the following identity: n 2 2n Σ (1)² - (²). = k=0 (1) Perhaps it seems mysterious? But if you try a few small values of n, you may begin to suspect it is correct. (a) Suppose n€ N and that we have a set S of cardinality 2n containing n distinct objects, all coloured red, and n distinct objects, all coloured blue. Let k = Z satisfy 0 < k < n. How many ways are there to sample n objects from S, subject to k of them being red? Briefly justify your answer.
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