i How many different ways can the podium be arranged? (The podium has a spot for only the 1st, 2nd and 3rd place horse)

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.6: Binomial Theorem
Problem 2SE: What role do binomial coefficients play in a binomial expansion? Are they restricted to any type of...
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Question
Simplify each binomial coefficient or permutations to factorial fractions:
(:)
n!
n!
P(n, k) =
k
(n – k)!k!
(n – k)!
You need not simplify these expressions, such as 154 or 17!, in your response.
Transcribed Image Text:Simplify each binomial coefficient or permutations to factorial fractions: (:) n! n! P(n, k) = k (n – k)!k! (n – k)! You need not simplify these expressions, such as 154 or 17!, in your response.
Horse Race 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?
Transcribed Image Text:Horse Race 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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