Question
Ezra is studying coins. He wants to know what everyone’s two favorite coins are from a group of 5: pennies, nickels, dimes, quarters, and half-dollars. How many ways can people choose their 1st- and 2nd-place choices?(1 point)
Responses
12 combinations
12 combinations
60 combinations
60 combinations
20 combinations
20 combinations
9 combinations
Responses
12 combinations
12 combinations
60 combinations
60 combinations
20 combinations
20 combinations
9 combinations
Answers
GPT-4o mini
To determine how many ways people can choose their 1st- and 2nd-place choices from a group of 5 coins (pennies, nickels, dimes, quarters, and half-dollars), we need to consider that the choices are ordered (since 1st and 2nd place are distinct).
1. Choose the 1st place coin: There are 5 options (the 5 different coins).
2. Choose the 2nd place coin: After selecting the 1st place coin, there are 4 remaining options.
Thus, the total number of combinations is calculated as follows:
\[
\text{Total combinations} = \text{Choices for 1st place} \times \text{Choices for 2nd place} = 5 \times 4 = 20
\]
Therefore, the answer is:
**20 combinations**.
1. Choose the 1st place coin: There are 5 options (the 5 different coins).
2. Choose the 2nd place coin: After selecting the 1st place coin, there are 4 remaining options.
Thus, the total number of combinations is calculated as follows:
\[
\text{Total combinations} = \text{Choices for 1st place} \times \text{Choices for 2nd place} = 5 \times 4 = 20
\]
Therefore, the answer is:
**20 combinations**.