Ten horses run in a race. How many different arrangements of placing 1st, 2nd , 3rd?
I tried by doing 10!over 7! But I don't know if that is correct , also how can you tell the finishing number as well.
10 different horses can come in 1st
then 9 different horses come in 2nd, and
then 8 different horse come in 3rd
so number of ways = 10(9)(8) = 720
btw, 10!/7! = 10*9*8*7!/7! = 10*9*8 = 720, which was your answer, so you are right
Yes this is correct thq dear
To calculate the number of different arrangements of placing 1st, 2nd, and 3rd in a race with 10 horses, you can use the concept of permutations.
The first-place finisher can be chosen from any of the 10 horses. Once the first-place horse is chosen, there are then 9 remaining horses to choose from for the second place. Finally, after choosing the first and second-place horses, there are 8 remaining horses to choose from for the third place.
To calculate the total number of arrangements, you multiply the number of choices for each place: 10 * 9 * 8 = 720.
So, there are 720 possible different arrangements of placing 1st, 2nd, and 3rd in the race with 10 horses.
To determine the actual finishing numbers, you would need additional information, such as the order in which the horses finish the race.
To find the number of different arrangements of placing 1st, 2nd, and 3rd, we can use the concept of permutations.
The number of arrangements of placing 1st, 2nd, and 3rd can be calculated by multiplying the number of choices for each position.
For the first position (1st place), there are 10 horses to choose from.
For the second position (2nd place), after the 1st place has been decided, there are 9 horses remaining to choose from.
For the third position (3rd place), after the 1st and 2nd places have been decided, there are 8 horses remaining to choose from.
To get the total number of arrangements, we multiply these numbers together:
10 * 9 * 8 = 720
So there are 720 different arrangements of placing 1st, 2nd, and 3rd in a race with 10 horses.
Now, to address your calculation attempt, you mentioned using "10! over 7!". However, this formula is incorrect for this scenario. The formula you were thinking of, "n! over (n-r)!", is used for calculating permutations without repetition, where r objects are selected from a set of n objects and the order matters. In this case, we are looking for the number of different orders (arrangements) of placing horses in 1st, 2nd, and 3rd, so the correct formula to use is simply multiplying the number of choices for each position as explained above.
To determine the finishing number for each horse in a race, you would typically look at the order in which they cross the finish line. The horse that crosses the finish line first would be in 1st place, the horse that crosses second would be in 2nd place, and so on.