There are 8 cars in a race. In how many ways can the cars finish first, second, third, and fourth? (Assume there are no ties.)
Well, there are 8 cars in the race, so let's think about this. For the first place, any car can win, so we have 8 possibilities. For the second place, there are now only 7 cars left, since one of them already finished first. So, we have 7 possibilities for the second place. Similarly, for the third place, there are 6 cars left, and for the fourth place, there are 5 cars left. Therefore, we can calculate the number of ways as: 8 * 7 * 6 * 5 = 1,680 ways. That's a lot of cars racing around, hope they don't run out of gas!
To calculate the number of ways the cars can finish first, second, third, and fourth, we need to determine the number of options for each position.
For the first position, any of the 8 cars can finish first, so there are 8 options.
After the first car has finished, there are 7 remaining cars left to choose from for the second position.
Similarly, for the third position, there would be 6 remaining cars, and for the fourth position, there would be 5 remaining cars.
Therefore, the total number of ways the cars can finish first, second, third, and fourth is calculated as:
8 x 7 x 6 x 5 = 1,680 possible ways
To find the number of ways the cars can finish first, second, third, and fourth, we can use the concept of permutations.
Since there are 8 cars racing, there are 8 possibilities for the first car to finish. Once the first car has finished, there are 7 remaining cars to choose from for the second place. Once the first two cars have finished, there are 6 remaining cars to choose from for the third place. Finally, once the first three cars have finished, there are 5 remaining cars to choose from for the fourth place.
To calculate the total number of ways the cars can finish, we multiply these numbers together:
Total number of ways = (Number of ways for the first place) × (Number of ways for the second place) × (Number of ways for the third place) × (Number of ways for the fourth place)
Total number of ways = 8 × 7 × 6 × 5 = 1680
Therefore, there are 1680 ways the cars can finish first, second, third, and fourth in the race.