## Thinking Mathematically (6th Edition)

The total number of proper subsets is $31$.
The set of coins worth less than a dollar is: {penny, nickel, dime, quarter, half dollar} A set of $n$ elements has $2^n$ subsets. This set has 5 elements, therefore it has $2^5=32$ subsets. However, we are asked for distinct subsets; therefore we have to take 1 from the result, as one of the subsets is going to be the set itself. The total number of proper subsets is $32-1=31$.