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

`Probability = (1)/(3)`

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 = (n(Factor))/(n(Set))`

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

`Probability = (8)/(24)`

Simplify to lowest term

`Probability = (1)/(3)`