Write a general rule/formula for finding the # segments that can be named by a given # of points on a line.?

Question

Write a general rule/formula for finding the # segments that can be named by a given # of points on a line.?

Answer 1

(n+2) C 2 = (n+2)! / (2! * n!)

you have to add 2 to n because both the endpoints of the line segment as part of our calculation to the number of segments that it is divided into

and each of these (n+2) points can make different combination of lines with any 2 points so we use the combination possibility

lets say there is only 1 point, we clearly see 3 distinct parts

using formula

we get 3C2 = 3 verifying formula



hope this helps

Answer 2

if there are n points on a line, then

n C 2 = n! / (2! (n-2)!)

segments can be named.