Chapter 0.4, Problem 3E

To determine

To find: the different ways to select the attire for prom once choose from three types of pants and six colors of vests.

Answer to Problem 3E

The number of possible combinations can be $18$ .

Explanation of Solution

Given:

Dane has chosen a jacket for prom, it must $3$ pants and $6$ colors of vests.

Concept used:

The number of ways of arranging $n$ different item in order is $n_1\times n_2\times n_3\times \mathrm{....}{n}_n$ .

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:

Consider Dane has chosen a jacket for prom, it must $3$ pants and $6$ colors of vests. The number of ways to select his attire by the use of fundamental counting principle as follows.

Number of ways $=3\text{ pants}\times 6\text{ vests}$ .

Simplifying it as follows:

  $=3\times 6=18$ .

Hence, the number of possible combinations can be $18$ .