n -r Prove that („",) : r+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...
icon
Related questions
Topic Video
Question
### Proving the Binomial Coefficient Identity

**Statement to Prove:**
\[
\binom{n}{r+1} = \frac{n-r}{r+1} \binom{n}{r}
\]
by computing the symbol on the left-hand side to be equal to the symbol on the right-hand side of the equality.

**Hint:**
Compute the left-hand side until you get the right-hand side with \( \binom{n}{n-r} \) instead. Then use the lecture notes on the binomial theorem section to finish the problem. At least that's how I did it.
Transcribed Image Text:### Proving the Binomial Coefficient Identity **Statement to Prove:** \[ \binom{n}{r+1} = \frac{n-r}{r+1} \binom{n}{r} \] by computing the symbol on the left-hand side to be equal to the symbol on the right-hand side of the equality. **Hint:** Compute the left-hand side until you get the right-hand side with \( \binom{n}{n-r} \) instead. Then use the lecture notes on the binomial theorem section to finish the problem. At least that's how I did it.
Expert Solution
steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON