The question is an illustration of permutation and combinations.
The number of lines from 7 dots is 21.
Given
[tex]n = 7[/tex] --- number of dots
[tex]r= 2[/tex] ----- 2 points make a line
The number of lines is calculated using the following formula:
[tex]Lines = \frac{n \times (n -1)}{2}[/tex]
So, we have:
[tex]Lines = \frac{7 \times (7 -1)}{2}[/tex]
Subtract 1 from 7
[tex]Lines = \frac{7 \times 6}{2}[/tex]
Divide 6 by 2
[tex]Lines = 7 \times 3[/tex]
Multiply 7 and 3
[tex]Lines = 21[/tex]
Hence, the number of lines is 21.
Read more about permutation and combinations at:
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