The five points A, B, C, D, and E are located on a circle, as shown below. How many line segments having two of these points as endpoints can be drawn?
4 + 3 + 2 + 1 = ?
To find the number of line segments that can be drawn with two points as endpoints, we need to determine the number of possible pairs of the five points.
We can use the combination formula to calculate this. The formula for calculating combinations is given by:
nCr = n! / (r!(n-r)!)
In this case, we need to find the number of combinations of 5 points taken 2 at a time, which is denoted as 5C2.
Using the combination formula:
5C2 = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3!) / (2!3!)
= (5 * 4) / (2 * 1)
= 10
Therefore, the number of line segments that can be drawn with two points as endpoints is 10.
To determine the number of line segments that can be drawn using two of the five points A, B, C, D, and E as endpoints, we can use the concept of combinations.
Combinations help us calculate the number of ways to choose a certain number of items from a larger set, without regard to the order in which they are chosen.
In this case, we want to choose 2 points out of the given 5 points (A, B, C, D, and E) to form a line segment.
The formula to calculate combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items and r is the number of items to be chosen.
Applying this formula, we have:
C(5, 2) = 5! / (2! * (5 - 2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / (2 * 1)
= 10
Therefore, there are 10 line segments that can be drawn using two of the given points as endpoints.