Thirteen people are entered in a race. If there are no ties, in how many ways can the first three places be awarded?

13P3 = 13*12*11

To calculate the number of ways the first three places can be awarded, we can use the concept of permutations.

There are 13 people competing for the first position. So, there are 13 possibilities for the first position.

After the first position is filled, there are 12 people remaining for the second position. Therefore, there are 12 possibilities for the second position.

Following the same logic, for the third position, there will be 11 possibilities remaining.

To calculate the total number of arrangements, we multiply the number of possibilities for each position together:

13 * 12 * 11 = 1,716

Thus, there are 1,716 ways the first three places can be awarded when there are no ties.

To determine the number of ways the first three places can be awarded in a race with thirteen people, you can use the concept of permutations.

In this case, we are interested in the number of ways to select the first three places out of thirteen people without any ties.

The first place can be awarded to any of the thirteen people. Once the first place is determined, there are twelve remaining people who can be awarded the second place. Finally, once the first two places are determined, there are eleven remaining people who can be awarded the third place.

Hence, the number of ways to award the first three places is calculated as follows:

13 options for the first place × 12 options for the second place × 11 options for the third place = 13 × 12 × 11 = 1,716.

Therefore, there are 1,716 ways the first three places can be awarded in the race without any ties.