In a local dog show, there are prizes for first, second, and third place. If there are 18 dogs competing, how many ways are there to award the prizes (assuming no dog can win two prizes)?
to do this, first we know that there are 18 ways for the first place (since there are 18 dogs), then 17 ways for the second place (18-1=17 since no dog can win two places), and 16 ways for the third. thus, we multiply these to get the number of ways:
18*17*16 = 4896 ways
hope this helps~ :)
To determine the number of ways to award the prizes, we can use the concept of permutations.
Since there are 18 dogs competing, there are 18 possible dogs to choose from for the first-place prize. After one dog has been awarded first place, there will be 17 remaining dogs eligible for the second-place prize. Finally, after the dog has been awarded the second-place prize, there will be 16 remaining dogs eligible for the third-place prize.
To calculate the total number of ways to award the prizes, we multiply the number of choices at each step:
Total ways = 18 * 17 * 16
Multiplying the numbers, we get:
Total ways = 4896
Therefore, there are 4896 ways to award the prizes in the local dog show.