Question

Create two different real-world scenarios—one in which you would use permutations and one in which you would use combinations: Include specific details and an explanation about what makes each situation either a combination or permutation.
Provide sample data and calculate the total number of possible permutations and combinations for both scenarios.

Answer 1

Permutation: In a race of 10 students, find the number of ways students can finish 1st, 2nd, and 3rd. In this case the order matters, so it is a permutation.
10 x 9 x 8 = 720 ways

Combination: In a class of 10 students, find the number of ways a group of 3 students can be selected to win a prize. In this case the order doesn't matter, so it's a combination.
10 x 9 x 8 / (3 x 2 x 1) = 120 ways