What is the total number of segments that can be formed by connecting any two points among six points?

What is the total number of segments that can be formed by connecting any two points among six points?

• A. 12
• B. 15
• C. 20
• D. 30

Answer: (B)

To determine the total number of segments that can be formed by connecting any two points among six points, we can use the formula for combinations. A line segment is determined by choosing 2 points from a set, and the number of ways to choose 2 points from \( n \) points is given by the combination formula: \[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \] In this case, \( n \) is 6 (the total number of points), and \( r \) is 2 (since we need to choose 2 points to form a segment). Plugging in these values, we get: \[ \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = \frac{30}{2} = 15 \] Thus, the total number of segments that can be formed by connecting any two points among the six points is 15. This indicates that for every pair of points, a unique segment can be drawn. Therefore, the correct answer is indeed 15 segments.

To determine the total number of segments that can be formed by connecting any two points among six points, we can use the formula for combinations. A line segment is determined by choosing 2 points from a set, and the number of ways to choose 2 points from ( n ) points is given by the combination formula:

[

\binom{n}{r} = \frac{n!}{r!(n-r)!}

]

In this case, ( n ) is 6 (the total number of points), and ( r ) is 2 (since we need to choose 2 points to form a segment). Plugging in these values, we get:

[

\binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = \frac{30}{2} = 15

]

Thus, the total number of segments that can be formed by connecting any two points among the six points is 15. This indicates that for every pair of points, a unique segment can be drawn. Therefore, the correct answer is indeed 15 segments.