Question

In Exercises 5–36, express all probabilities as fractions.

Teed Off When four golfers are about to begin a game, they often toss a tee to randomly select the order in which they tee off. What is the probability that they tee off in alphabetical order by last name?

Short answer

The probability that the golfers tee off in alphabetical order by the last name is $\frac{1}{24}$.

Step-by-step solution

Given information

Four golfers toss a tee to decide the order in which they tee off.

Define factorial

The total number of possible arrangements of a given set of units (n) is computed using thefactorialformula.

$n!=n\times \left(n-1\right)\times \left(n-2\right)\times ...1$

Calculation

Let A be the event that the golfers tee off in alphabetical order of the last name.

The total number of ways in which they can tee off is calculated below:

$$\begin{gathered} 4!=4\times 3\times 2\times 1 \\ =24 \end{gathered}$$

The number of ways in which they can tee off in alphabetical order is one.

The probability that the golfers tee off in alphabetical order of the last name

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{ways}}{\text{Total}\text{number}\text{of}\text{ways}} \\ =\frac{1}{24} \end{gathered}$$

Therefore, the probability that the golfers tee off in alphabetical order of the last name is equal to $\frac{1}{24}$.