Suppose that 12 people enter a swim meet. Assuming that there are no ties, in how manyways could the gold, silver, and bronze medals be awarded?

To solve this problem, we need to use the concept of permutations.

Step 1: Determine the number of ways to award the gold medal. There are 12 swimmers, so there are 12 ways to award the gold medal.

Step 2: Determine the number of ways to award the silver medal. After the gold medal has been awarded, there are 11 remaining swimmers. So, there are 11 ways to award the silver medal.

Step 3: Determine the number of ways to award the bronze medal. After the gold and silver medals have been awarded, there are 10 remaining swimmers. So, there are 10 ways to award the bronze medal.

Step 4: Multiply the number of ways to award each medal to find the total number of ways to award all three medals.

So, the total number of ways to award the medals is 12 * 11 * 10 = 1320 ways.