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Chapter 4: Q14 (page 174)

In Exercises 5鈥�36, express all probabilities as fractions.

Electricity When testing for current in a cable with five color-coded wires, the author used a meter to test two wires at a time. How many different tests are required for every possible pairing of two wires?

Short Answer

Expert verified

The number of tests required for testing every possible pair is equal to 10.

Step by step solution

01

Given information

There are five color-coded wires. Two wires are paired each time to test the current in a cable.

02

Define combination

The combination is used to determine the total ways of choosing r items out of the nitemswithout replacing the order of the items and considering the order of the items.

Mathematically, the formula of combination is as follows:

Crn=n!n-r!r!

03

Calculation

The number of different wires is five.

The total number of ways in which a pair of wires from five different wires can be selected without replacement is computed as shown below:

5C2=5!5-2!2!=10

Therefore, the number of tests required for each pair is equal to 10.

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