Create two problems for your fellow students to solve. Make one of the questions a permutation and the other one a combination.

The permutation I gave this example. In how many ways can we arrange 8 movies on a book self?

The combination example I put. How many ways can this problem be solved? A teacher has 20 individual students and she wants to pull 6 students out of class to help tutor other students.

Can you tell me if I did this right?

3 answers

Yup, that's right :)

Thank you

Yes, you did it right! You provided one example of a permutation question and another example of a combination question. Permutations involve the arrangement or ordering of objects, while combinations involve selecting a subset of objects without regard to the order. Let's break down both of the problems you created:

Permutation: In how many ways can we arrange 8 movies on a bookshelf?
To solve this problem, we can use the formula for permutations: P(n, r) = n! / (n - r)!. Here, n represents the total number of movies, and r represents the number of movies we want to arrange. In this case, n = 8 (since we have 8 movies) and r = 8 (since we want to arrange all the movies). Plug these values into the formula: P(8, 8) = 8! / (8 - 8)! = 8! / 0! = 8! / 1 = 8! = 40320. Therefore, there are 40,320 ways to arrange the 8 movies on the bookshelf.

Combination: How many ways can this problem be solved? A teacher has 20 individual students, and she wants to pull 6 students out of class to help tutor other students.
To solve this problem, we can use the formula for combinations: C(n, r) = n! / (r! * (n - r)!). Here, n represents the total number of students, and r represents the number of students the teacher wants to select. In this case, n = 20 (since there are 20 individual students) and r = 6 (since the teacher wants to select 6 students). Plug these values into the formula: C(20, 6) = 20! / (6! * (20 - 6)!) = 20! / (6! * 14!) = (20 * 19 * 18 * 17 * 16 * 15) / (6 * 5 * 4 * 3 * 2 * 1) = 38,760. Therefore, there are 38,760 ways to select 6 students out of 20 for tutoring.