Chapter 13.2, Problem 9PPS

To determine

To find: the probability that a randomly generated number is $25938$ .

Answer to Problem 9PPS

The probability is $\frac{1}{15120}$ .

Explanation of Solution

Given:

The number consist of $5$ digits ranging from $1-9$ .

Concept used:

According to the combination formula:

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

Where $C$ is the combination.

  $n$ is the total number of objects in the set.

  $r$ is the total number of objects in the set.

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

Calculation:

The number of possible outcomes is the number of arrangements of $9$ digits taken at a time.

  $C{}_5=\frac{9!}{\left(9-5\right)!}=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!}=15,120$ .

The only favorable outcome is the arrangement $25398$ .therefore the probability is $\frac{1}{15120}$ .

Hence, the probability is $\frac{1}{15120}$ .