Chapter 13.2, Problem 16PPS

To determine

To find: the probability that chosen city is Austin, Cheyenne and Savannah.

Answer to Problem 16PPS

The probability is $\frac{1}{455}$ .

Explanation of Solution

Given:

Rita choose the three random photos from $15$ cities.

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 choosing $3$ cities from a set of $15$ cities and order is not important. So, the number of possible outcomes is:

  $C{}_3=\frac{15!}{\left(15-3\right)!\left(3\right)!}=455.$

The number of favorable outcomes is only one of choosing the cities Austin, Cheyenne and Savannah.

Therefore, the probability is $\frac{1}{455}$ .

Hence, the probability is $\frac{1}{455}$ .