Question

example 1
determine the total number of subsets
apples, grapes, peaches, plums, and strawberries are available for dessert.
how many different combinations of fruit can be made for dessert?

Explanation:

Step1: Recall subset - formula

The formula for the number of subsets of a set with \(n\) elements is \(2^n\). Here, the set of fruits has \(n = 5\) elements (apples, grapes, peaches, plums, strawberries).

Step2: Calculate the number of subsets

Using the formula \(2^n\), substitute \(n = 5\). So, \(2^5=2\times2\times2\times2\times2 = 32\). But we usually exclude the empty - set when talking about combinations of fruits for dessert. So the number of non - empty subsets is \(2^n-1\).
\(2^5 - 1=32 - 1=31\).

Answer:

31