Question

How many permutations of three items can be selected from a group of six? Use the letters $A$, $\mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E},$ and $\mathrm{F}$ to identify the items, and list each of the permutations of items $\mathrm{B}, \mathrm{D},$ and $\mathrm{F}$.

Name: Problem 3, Chapter 4: Statistics for Business Economics
Uploaded: 2023-10-01T21:29:45-08:00
Duration: 1 min 39 s
Channel: Sheryl Ezze
Description: How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

   How many permutations of three items can be selected from a group of six? Use the letters $A$, $\mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E},$ and $\mathrm{F}$ to identify the items, and list each of the permutations of items $\mathrm{B}, \mathrm{D},$ and $\mathrm{F}$.

Statistics for Business Economics

David R. Anderson,… 11th Edition

Chapter 4, Problem 3

Instant Answer

Solved by Expert Sheryl Ezze

10/01/2023

Step 1

In permutations, order is important. So, we use the formula for permutations which is $nPm = \frac{n!}{(n-m)!}$ where $n$ is the total number of items and $m$ is the number of items to select. Here, $n=6$ and $m=3$. Show more…

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How many permutations of three items can be selected from a group of six? Use the letters $A$, $\mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E},$ and $\mathrm{F}$ to identify the items, and list each of the permutations of items $\mathrm{B}, \mathrm{D},$ and $\mathrm{F}$.

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Key Concepts

Factorial

A factorial, denoted by an exclamation mark (n!), is the product of all positive integers less than or equal to n. Factorials are a fundamental component in the mathematical calculation of permutations and combinations.

Enumeration of Permutations

Enumeration of permutations involves systematically listing all possible ordered arrangements of a set of items. This process is useful for verifying calculations and understanding the structure of the solution space in permutation problems.

Permutation

A permutation is an ordered arrangement of items where the order matters. This concept is widely used in combinatorics to determine how many different sequences can be formed when selecting items from a set.

Permutation Formula

The permutation formula, P(n, r) = n! / (n - r)!, is used to calculate the number of ways to arrange r items from a total of n distinct items. This formula takes into account that the order of arrangement is important.

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