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Letr be a real number and let k be an integer. We then define the binomial coefficient () by (3) r(r-1)(r-k+1) k! 1 0 if k 21 if k = 0 if ks-1.

Letr be a real number and let k be an integer. We then define the binomial coefficient () by (3) r(r-1)(r-k+1) k! 1 0 if k 21 if k = 0 if ks-1.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Letr be a real number and let k be an integer. We then define the binomial coefficient () by = r(r-1)(r-k+1) k! 0 if k 21 if k = 0 if k ≤ -1.
Transcribed Image Text:Letr be a real number and let k be an integer. We then define the binomial coefficient () by = r(r-1)(r-k+1) k! 0 if k 21 if k = 0 if k ≤ -1.
1. For any real number r and any integer r #k, show that a) ()=(¹), and b) () = (-1)k (r+k-1). Hint: use the definition of () from Page 137. r-k
Transcribed Image Text:1. For any real number r and any integer r #k, show that a) ()=(¹), and b) () = (-1)k (r+k-1). Hint: use the definition of () from Page 137. r-k
Expert Solution
Step 1

The Binomial coefficient is defined as:

rk=rr-1...r-k+1k! for k≥1 

k is an integer and r is a real number.

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