Respuesta :
To find out how many different triangles can be formed with 7 distinct points on a plane, we can use the concept of combinations.
1. To form a triangle, we need 3 points. With 7 distinct points, we can choose 3 points out of the 7 in different ways to create triangles.
2. The number of ways to choose 3 points out of 7 is calculated using the combination formula, denoted as "C(n, k)" or "n choose k". The formula is: C(n, k) = n! / (k! * (n - k)!), where "!" denotes factorial.
3. Substituting the values into the formula, we get: C(7, 3) = 7! / (3! * (7 - 3)!) = 35.
Therefore, with 7 distinct points on a plane, it is possible to form 35 different triangles. Each combination of 3 points forms a unique triangle, resulting in 35 different possible triangles that can be formed.
Answer:
Therefore, with 7 distinct points on a plane, 35 different triangles can possibly be formed. Each triangle will have a unique combination of the 3 points chosen from the 7 available points.
Step-by-step explanation:
To find the number of different triangles that can be formed using 7 distinct points on a plane, we need to consider the combination of these points.
Here's how we can approach this problem:
1. To form a triangle, we need 3 points. With 7 distinct points, we can choose 3 points out of 7 in a way that the order of selection does not matter. This is a combination problem.
2. The number of ways to choose 3 points out of 7 can be calculated using the combination formula, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, n = 7 and k = 3.
3. Calculating the number of triangles:
C(7, 3) = 7! / (3! * (7 - 3)!)
= 7! / (3! * 4!)
= 35
Therefore, with 7 distinct points on a plane, 35 different triangles can possibly be formed. Each triangle will have a unique combination of the 3 points chosen from the 7 available points.
