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? Need help solving this problem, it's all one problem **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.

(i). Find the number of different ways in which the podium can be arranged: Total number of horses…

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?

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?

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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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

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?

Need help solving this problem, it's all one problem

**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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