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...
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### 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.
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