A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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A horse race has 12 horses.
i ) How many dierent ways can the podium be arranged? (The podium has a spot for only the 1st, 2nd and 3rd place horse)
ii ) How many different ways can the horses finish the race such that Grand Valor, Seabiscuit and Secretariat do not finish first?
iii ) How many dierent ways can the horses nish the race such that one horse (Grand Valor) always beats both Seabiscuit and Secretariat?
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![**Educational Content: Simplifying Binomial Coefficients and Permutations**
This section focuses on simplifying binomial coefficients and permutations to factorial fractions. Here's how you can express them mathematically:
1. **Binomial Coefficient**:
\[
\binom{n}{k} = \frac{n!}{(n-k)!k!}
\]
2. **Permutation**:
\[
P(n, k) = \frac{n!}{(n-k)!}
\]
For simplification, you do not need to further simplify expressions like \(15^4\) or \(17!\) in your calculations.](https://content.bartleby.com/qna-images/question/8cb58778-70ba-4f7e-90ce-7267bd79a013/e2a21255-0fb7-4e0a-9c1d-78f8a248b525/5mgujlp_processed.jpeg)
Transcribed Image Text:**Educational Content: Simplifying Binomial Coefficients and Permutations**
This section focuses on simplifying binomial coefficients and permutations to factorial fractions. Here's how you can express them mathematically:
1. **Binomial Coefficient**:
\[
\binom{n}{k} = \frac{n!}{(n-k)!k!}
\]
2. **Permutation**:
\[
P(n, k) = \frac{n!}{(n-k)!}
\]
For simplification, you do not need to further simplify expressions like \(15^4\) or \(17!\) in your calculations.
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