Answer:
there are 1,716 ways for Miguel to choose the best, second-best, and third-best essays out of 13 entries.
Explanation:
If Miguel has to select the best, second-best, and third-best essays out of 13 entries, the number of ways he can choose them is calculated using the concept of permutations.
The number of ways to choose the best essay is 13 (because there are 13 choices).
Once the best essay is selected, there are 12 remaining essays for the second-best position.
After the first two are chosen, there are 11 remaining essays for the third-best position.
Therefore, the total number of ways Miguel can choose the top three essays is given by the product:
Number of ways=13×12×11
Number of ways=1,716
So, there are 1,716 ways for Miguel to choose the best, second-best, and third-best essays out of 13 entries.