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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 is123,124,132,134,142,143,213,214,

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

01

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).

02

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

03

Step 3. Determine the value of permutation.

We know that,

P(n,r)=n!(n-r)!

Using the above formula, we get

P(4,3)=4!(4-3)!=4!1!=4脳3脳2脳11=24

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