Question

A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.

Answer 1

Answer:

$Probability = \frac{1}{3}$

Step-by-step explanation:

Given

$Set:\ \{1, 2, 3, \ldots, 24\}$

$n(Set) = 24$

Required

Determine the probability of selecting a factor of 4!

First, we have to calculate 4!

$4! = 4 * 3 * 2 * 1$

$4! = 24$

Then, we list set of all factors of 24

$Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}$

$n(Factors) = 8$

The probability of selecting a factor if 24 is calculated as:

$Probability = \frac{n(Factor)}{n(Set)}$

Substitute values for n(Set) and n(Factors)

$Probability = \frac{8}{24}$

Simplify to lowest term

$Probability = \frac{1}{3}$