Answer
45 line segments are needed .
Work Step by Step
There are 10 points for figure 2.Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 10 for N and 2 for R:
$_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$
$_{10}$C$_{2}$=$\frac{10!}{2!(10-2)!}$ -simplify like terms-
$_{10}$C$_{2}$=$\frac{10!}{2! (8!)}$ -write using factorial-
$_{10}$C$_{2}$=$\frac{10*9*8*7*6*5*4*3*2*1}{(2*1)(8*7*6*5*4*3*2*1)}$ -simplify-
$_{10}$C$_{2}$=45
We need 45 line segments to join each point for figure 2.
