Question

Counting Problem

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{There are \(10\) points in a plane of which \(4\) are collinear. }\hspace{.33em}\\~\\
& \normalsize \text{No other \(3\) points are collinear.}\hspace{.33em}\\~\\
& \normalsize \text{Find the number of lines that can be drawn .}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

is the answer \(\dbinom{6}{2} + 6*4\) ?

Answer 3

10C2-4C2+1

Answer 4

right, both are same just a +1 is missing in my earlier reply

Answer 5

how u got that

Answer 6

forget about 4 collinear points

Answer 7

then you have 6 points,

you know that any two points determine a line

so how many lines can you make using 6 points ?

Answer 8

6c2

Answer 9

next, from each of these 6 points, you can draw a line to each of the 4 collinear points, yes ?

Answer 10

yes

Answer 11

how many lines can you draw from those 6 points to those 4 collinear points ?

Answer 12

6C4

Answer 13

nope, notice that from each of those 6 points, you can draw exactly 4 lines to those collinear points

Answer 14

4*6

Answer 15

Yes, so far the count is \(\dbinom{6}{2}+4*6\)

can you guess the one line that is missing ?