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Agency Cases An investigative agency has 7 cases and 5 agents. How many different ways can the cases be assigned if only 1 case is assigned to each agent?

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

Piedmont College

University of St. Thomas

Idaho State University

Lectures

0:00

00:31

From a pool of 7 secretari…

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A team of 4 officers is se…

00:54

A professor grades homewor…

00:27

How many different ways ar…

02:16

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02:14

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01:52

Establishing Committees In…

00:56

In how many ways can 5 pla…

00:30

In how many ways can 7 peo…

01:19

In how many ways can 5 dif…

08:35

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01:36

Suppose that a department …

02:49

Stacking Boxes In how many…

01:32

Use any or all of the meth…

00:40

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04:46

How many ways are there to…

00:21

01:09

02:42

Use the fundamental princi…

So this problem is an application off permutation Rule number one. So there are seven cases in five agents in an investigative agency and how many different ways skin the cases be assigned. If each agent can only have one case, let's review the permutation. Rule number one. This says that the number of permutations off in objects taken on at the time, given that order is important, would equal to and factorial over n minus r factorial and take noted in this particular problem, order is important. For example, if we assign cases in this form Agent one agent to Agent free Agent four Agent five Let's say are assigned cases Case one case too. Case three case for case five this will be considered a different assignment of cases compared to if Agent One was the sign. Case five Agent to case four. Agent three, Case three Agent four case to an agent five case one. So order is important in this case. Now, to answer the question, there are seven cases, five agents. So the number or the permutation number of permutations of seven taken five at the time we're orders important is equal to seven factorial over seven minus five. Victoria is this seven factorial over two factorial and using a calculator. This is equal to 2520 different ways off assigning the cases.

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