Chapter 13.2, Problem 15PPS

To determine

To find: the probability that chosen photo is at the right.

Answer to Problem 15PPS

The probability is $\frac{1}{10626}$ .

Explanation of Solution

Given:

Placing $24$ photos randomly.

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:

Here by choosing $4$ photos from a set of $24$ photos, and the $4$ chosen photos can be placed in any order. So, the number of possible outcomes is:

  $C{}_4=\frac{24!}{4!\left(24-4\right)!}=\frac{24\times 23\times 22\times 21\times 20!}{20!\times 4\times 3\times 2\times 1}=10626.$

There is only one favorable outcome. Therefore, the probability is $\frac{1}{10626}$ .

Hence, the probability is $\frac{1}{10626}$ .