Decide if it's permuatation or combination .

1-how many teams of 4 horses be made if there were 9 horses in total ?

2-mike has nice baseball trophies to arrange on the shelf . How many different ways can be arranged ?

3-in a math class , there are 24 students,the teacher picks 4 students to help do a demonstration.how many diffrent groups of 4 could she have chosen ?

1. We can't tell from the question. If the position of a particular horse in the team is important, then it is a permutation. If you just care about groups of 4 horses, then you have a combination. I think the placement of a horse should be important

2. combination

3. combination, unless members of the group have specific tasks in the demonstration.

1. Permutation: 9x8x7x6 = P(9,4) = 3024
combination : C(9,4) = 126
2. 9!
3. C(24,4) = 10626

To determine whether the question involves permutations or combinations, we need to understand the difference between the two.

Permutations refer to arrangements or orderings of objects, where the order matters. In permutations, objects are selected one at a time without replacement. For example, the permutations of the letters "A", "B", and "C" would include "ABC", "ACB", "BAC", "BCA", "CAB", and "CBA".

Combinations, on the other hand, refer to selections of objects where the order does not matter. In combinations, objects are selected together without regard to their order. For example, the combinations of the letters "A", "B", and "C" would include "ABC", "ACB", "BAC", and "CAB", but exclude "BCA" and "CBA".

Now let's apply this understanding to the given questions:

1. How many teams of 4 horses can be made if there were 9 horses in total?
This question involves combinations since the order of the horses in a team does not matter. We can use the combination formula to find the answer. The notation "C(n, r)" represents the number of combinations of "r" objects chosen from a set of "n" objects.

In this case, we have 9 horses to choose from, and we want to select teams of 4 horses. Therefore, the number of teams of 4 horses that can be made is calculated as C(9, 4).

2. Mike has 9 baseball trophies to arrange on the shelf. How many different ways can they be arranged?
This question involves permutations since the order of the trophies on the shelf matters. We can use the permutation formula to find the answer. The notation "P(n, r)" represents the number of permutations of "r" objects chosen from a set of "n" objects.

In this case, we have 9 trophies to arrange on the shelf. Therefore, the number of different ways they can be arranged is calculated as P(9, 9).

3. In a math class, there are 24 students, and the teacher picks 4 students to help do a demonstration. How many different groups of 4 could she have chosen?
This question involves combinations since the order of the selected students does not matter. We can use the combination formula to find the answer. The notation "C(n, r)" represents the number of combinations of "r" objects chosen from a set of "n" objects.

In this case, there are 24 students, and the teacher wants to select groups of 4 students. Therefore, the number of different groups of 4 students she could have chosen is calculated as C(24, 4).