There are 12 different ways the gold and silver medals can be awarded among 4 finalists in a dog show. We multiply the 4 choices for gold medalist by the 3 remaining choices for silver medalist.
The question asks about the number of different ways the gold and silver medals can be awarded among 4 finalists in a dog show. This is a problem of permutations where order matters because the gold and silver medals are distinct.
First, we select a winner for the gold medal. There are 4 finalists, so there are 4 different choices for the gold medalist. Once the gold medal is awarded, we move on to the silver medal. There are now 3 remaining finalists who did not receive the gold medal. Therefore, there are 3 different choices for the silver medalist.
To find the total number of different ways to award the medals, we multiply the number of choices for the gold medal by the number of choices for the silver medal. Thus, the calculation to determine the different ways to award the medals is:
- Choose a gold medalist: 4 possibilities
- Choose a silver medalist: 3 possibilities (since one finalist has already been awarded the gold medal)
Multiplying the possibilities together, 4 (for gold) × 3 (for silver) gives us 12 different ways the medals can be awarded.
Therefore, there are 12 different combinations in which the two medals can be handed out to the finalists in the dog show.