Question

In Exercises 5–36, 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

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

Step-by-step solution

Given information

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

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:

${}^n{C}_r=\frac{n!}{\left(n-r\right)!r!}$

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:

$$\begin{gathered} {}^5{C}_2=\frac{5!}{\left(5-2\right)!2!} \\ =10 \end{gathered}$$

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