Question

Express all probabilities as fractions. In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third?

Name: Problem 8, Chapter 4: Elementary Statistics
Uploaded: 2020-10-12T17:05:08-08:00
Duration: 1 min 59 s
Channel: Harsh Gadhiya
Description: Express all probabilities as fractions. In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third?

   Express all probabilities as fractions.
In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third?

Elementary Statistics

Mario F. Triola 13th Edition

Chapter 4, Problem 8

Instant Answer

Solved by Expert Harsh Gadhiya

10/12/2020

Step 1

This is a combination problem, which can be solved using the combination formula: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where \(n\) is the total number of items, \(k\) is the number of items to choose, and "!" denotes factorial. Show more…

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Express all probabilities as fractions. In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third?

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Key Concepts

Combinations

Combinations refer to the selection of items from a larger set where the order of selection does not matter. In problems like selecting players for a team, the combination formula (n choose k) is used to count the number of ways to select k items from n without considering the order. It is a crucial concept in probability and combinatorial analysis because it simplifies counts where sequence is irrelevant.

Permutations

Permutations involve the arrangement of items where the order does matter. After selecting a subset of players, if we need to assign them specific roles or positions (such as first, second, and third), the number of arrangements is calculated using the permutation formula, typically involving factorials. This concept is key in scenarios where different orders represent distinct outcomes.

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