Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Problem 1: Combinatorial Calculations
Calculate the following binomial coefficients:
(a) \(\binom{8}{3}\)
(b) \(\binom{8}{0}\)
(c) \(\binom{8}{5}\)
(d) \(\binom{52}{50}\)
(e) \(\binom{52}{52}\)
(f) \(\binom{52}{1}\)
---
### Explanation
These expressions, known as binomial coefficients, are part of combinatorial mathematics and are used to calculate the number of ways to choose a subset of items from a larger set. The binomial coefficient \(\binom{n}{k}\) is calculated using the formula:
\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]
where \(n!\) (n factorial) is the product of all positive integers up to \(n\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc28801d2-5244-43a8-94e3-88d6acce7d2a%2F60423960-b9d6-416f-8861-3c5d6cfb147e%2Far7kta_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 1: Combinatorial Calculations
Calculate the following binomial coefficients:
(a) \(\binom{8}{3}\)
(b) \(\binom{8}{0}\)
(c) \(\binom{8}{5}\)
(d) \(\binom{52}{50}\)
(e) \(\binom{52}{52}\)
(f) \(\binom{52}{1}\)
---
### Explanation
These expressions, known as binomial coefficients, are part of combinatorial mathematics and are used to calculate the number of ways to choose a subset of items from a larger set. The binomial coefficient \(\binom{n}{k}\) is calculated using the formula:
\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]
where \(n!\) (n factorial) is the product of all positive integers up to \(n\).
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