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 and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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I need help with this problem and an explanation for the solution described below (Discrete mathematics)
4. Consider the following identity: 2 Σ(3) - (30) (2n). (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 E 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
Consider the following sets: A = {n € Z¹ | n² ≤ 9}, B = {2n | n ≤ Z¹}, C = {2,3,5,8}. For each proposition given below, determine the value of the integer x that satisfies that proposition. Simplify all answers completely. (x ≤ A) ^ (x ≤ B) ^ (x ≤ C') A/ (x ‡ A) ^ (x = B) ^ (x ≤ C') A/ (x ≤ A) ^ (x & B) ^ (x = C) (x ≤ A) ^ (x & B) ^ (x ‡ C) (x ‡ A) ^ (x & B) ^ (x ≤ C') A/
3. If |F|q 0.
plz solve the question 3 with explanation. i will give you upvote.
and Let A {x|x is a prime number and 10