Consider the following identity: n 2 2n Σ (1)² = (²7) 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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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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 ke 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 ke 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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