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

The Binomial coefficient is defined as: rk=rr-1...r-k+1k! for k≥1 k is an integer and r is a real…

Answered: Letr be a real number and let k be an…

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)

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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Question

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

Expert Solution

Step 1

The Binomial coefficient is defined as:

$(\begin{matrix} r \\ k \end{matrix}) = \frac{r (r - 1) . . . (r - k + 1)}{k!}$ for $k \geq 1$

k is an integer and r is a real number.

Step by step

Solved in 3 steps

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