Question

Football Teams A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed? (check your book to see image)

Name: Problem 56, Chapter 13: Precalculus
Uploaded: 2020-07-04T19:05:27-08:00
Duration: 1 min 40 s
Channel: Wesley Hines
Description: Football Teams A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed? (check your book to see image)

   Football Teams A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed?

(check your book to see image)

Precalculus

Michael Sullivan 9th Edition

Chapter 13, Problem 56

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Solved by Expert Wesley Hines

07/04/2020

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Football Teams A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed? (check your book to see image)

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Key Concepts

Combination

Combination is a key concept in combinatorial mathematics that refers to selecting items from a larger set where the order of selection does not matter. This concept is crucial when calculating the number of ways to choose players or objects from a group without considering the sequence in which they are chosen.

Binomial Coefficient

The binomial coefficient, often denoted as 'n choose k', is the mathematical notation used to represent the number of combinations possible when choosing k elements from a set of n distinct elements. This concept is vital for accurately determining counts in selection problems.

Multiplication Principle

The multiplication principle in counting states that if an event can occur in several independent stages, the total number of outcomes is the product of the number of choices at each stage. This principle is essential when combining separate choices from different categories to form a complete set.

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