To determine how many ways people can choose their first and second favorite coins from a group of 5 coins (pennies, nickels, dimes, quarters, and half-dollars), we need to calculate how many unique combinations of first and second choices can be made from the 5 options.
- For the first choice, there are 5 options (any of the 5 coins).
- After selecting the first choice, that coin cannot be chosen again for the second choice, leaving 4 remaining options.
Thus, the number of combinations can be calculated as:
\[ \text{Total combinations} = \text{choices for the first favorite} \times \text{choices for the second favorite} = 5 \times 4 = 20 \]
Therefore, the correct answer is 20 combinations.