   Chapter 14.CR, Problem 13E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 1-24 Counting These exercises involve counting.Tennis Games A group of friends has reserved a tennis court. They find that there are ten different ways in which two of them can play a singles game on this court. How many friends are in this group?

To determine

To find:

The number of friends.

Explanation

Given:

There are ten different ways in which two of them can play a singles game on the court.

Approach:

A combination of r objects from a set is any subset of the set that contains r elements (without regard to order).

If a set has n objects, then the number of combination of r elements from the set is denoted as C(n,r) and is called the number of combination of n objects taken r at a time. Then,

C(n,r)=n!r!(nr)! ……(1)

Calculation:

The total number of friends who can play a singles game on the court is 2, therefore r=2 chosen at a time for the tennis court in 10 different ways.

C=C(n,2) ……(2)

Calculate C(n,2)

Substitute n for n and 2 for r in equation (1).

C(n,2)=n!2!(n2)!

The number of ways in which two of them can play a single game on the court is 10.

C=10

This gives,

C(n,2)=10

Substitute (n!2!(n2)!) for C(n,2) in the above expression and calculate the value of n.

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