Question

The numbers 5, 6, 7, and 8 are randomly arranged to create a four-digit number. What is the probability that the number formed is not divisible by 4?

Answer 1

Using the arrangements and the probability concept, it is found that there is a 0.75 = 75% probability that the number formed is not divisible by 4.

• A probability is the number of desired outcomes divided by the number of total outcomes.

• The number of possible arrangements of n elements is given by $A_n = n!$

In this problem, there are 4 elements, hence $n = 4, T = A_4 = 4! = 24$.

A number is a multiple of 4 if the number composed by it's last 2 digits are multiples of 4.

• Hence, the possible options for the last 2 digits are: 56, 68, 76.

• For each of them, there are $A_2 = 2! = 2$ options for the first 2 digits, hence, there will be 2 x 3 = 6 multiples of 4.

The other 18 numbers formed are not divisible by 4, hence:

$p = \frac{18}{24} = 0.75$

0.75 = 75% probability that the number formed is not divisible by 4.

For more on arrangements and probabilities, you can check brainly.com/question/24437717