Chapter 13: Q. 25 (page 855)

List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is $P (4, 3)$ ?

Short Answer

Expert verified

The list of ordered arrangements is $123, 124, 132, 134, 142, 143, 213, 214,$

$231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 .$

The value of the given permutation is 24.

Step by step solution

Step 1. Given information.

3 objects are chosen from 4 objects 1, 2, 3, and 4 at a time without repetition.

The given permutation is $P (4, 3)$ .

Step 2. Determine the list of ordered arrangements.

The list of ordered arrangements is:

$123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432$

Step 3. Determine the value of permutation.

We know that,

$P (n, r) = \frac{n!}{(n - r)!}$

Using the above formula, we get

$\begin{array}{rcl} P (4, 3) & = & \frac{4!}{(4 - 3)!} \\ = & \frac{4!}{1!} \\ = & \frac{4 \times 3 \times 2 \times 1}{1} \\ = & 24 \end{array}$

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List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is $P (4, 3)$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the list of ordered arrangements.

Step 3. Determine the value of permutation.

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List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is P(4,3)?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the list of ordered arrangements.

Step 3. Determine the value of permutation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is $P (4, 3)$ ?