   Chapter 9.5, Problem 4TY ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# A formula relating ??? and ???is______

To determine

To fill in the blank in the statement, “ A formula relating (nr) and P(n,r) is _____.”

Explanation

Given information:

The statement is given as “A formula relating (nr) and P(n,r) is _____.”

Formula used:

The number of ways to select r number of ordered elements from a set of n number of elements is given by P(n,r)=n!(nr)!

If the number of elements in a set is n and the subsets formed from the set are with r elements.

The number of ways to select r elements from n number of elements is given by n!(nr)!

Also, by the notation (nr) we denote the number of r combinations from a set of n elements.

To calculate the number of r combinations, first we should know how many ways there are to select r elements from n elements. Then we consider the order of a selected elements.

In a set of r elements, there are r! of different arrangements within the elements. But for a combination, we do not care about the order and we consider all these arrangements as one combination.

Hence, we have to divide the number of selections by the number of arrangements to obtain the total number of r combinations

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