To determine the number of ways people can choose their 1st- and 2nd-place choices from 5 different coins, we need to calculate permutations since the order of choices matters (1st and 2nd are distinct).
- For the 1st-place choice, there are 5 options (pennies, nickels, dimes, quarters, and half-dollars).
- After selecting a coin for 1st place, there are 4 remaining options for the 2nd-place choice.
Thus, the total number of combinations is given by:
\[ 5 \text{ (choices for 1st place)} \times 4 \text{ (choices for 2nd place)} = 20 \]
Therefore, the answer is 20 combinations.