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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A horse race has 12 horses.
i) How many different 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 different ways can the horses finish the race such that one horse (Grand Valor) always beats both Seabiscuit and Secretariat?
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![Simplify each binomial coefficient or permutation to factorial fractions:
\[
\binom{n}{k} = \frac{n!}{(n-k)!k!} \quad \quad P(n, k) = \frac{n!}{(n-k)!}
\]
You need not simplify these expressions, such as \( 15^4 \) or \( 17! \), in your response.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cb58778-70ba-4f7e-90ce-7267bd79a013%2Ff1764604-5723-4929-bfbe-50a2ad0eb82a%2F5glwnnr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Simplify each binomial coefficient or permutation to factorial fractions:
\[
\binom{n}{k} = \frac{n!}{(n-k)!k!} \quad \quad P(n, k) = \frac{n!}{(n-k)!}
\]
You need not simplify these expressions, such as \( 15^4 \) or \( 17! \), in your response.
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