Chapter 11.1, Problem 11PPSE

Solution

To calculate: The number of different arrangements that are possible for the banquet and dance if the prom committee has four sites available for the banquet and three sites available for the dance.

The resultant value is 12 ways.

Given information:

The prom committee has four sites available for the banquet and three sites available for the dance.

Formula used: Fundamental Principle of counting says that if one event can occur in $m$ different ways and a second event can occur in $n$ different ways, then sequence of both events can occur in $m\cdot n$ different ways.

Calculation:

Consider the given information,

Sites available for the banquet: 4

Sites available for the dance: 3

It means there are four ways in which a site for banquet can be selected.

Similarly, there are three ways in which a site for dance can be selected

Now apply the Fundamental Principle of counting,

  $4\times 3=12$

Therefore, the total number of arrangements for banquet and dance are 12.