Question

There are 10 points and out of which 4 are collinear. How many different lines can be drawn ?

• A. ${}^{10}{C}_2{-}^4{C}_2$
• B. ${}^{10}{C}_2{-}^4{C}_2+1$
• C. ${}^{10}{C}_3{-}^4{C}_3+1$
• D. None of these

Answer 1

The correct option is B ${}^{10}{C}_2{-}^4{C}_2+1$

To drawn a line in a plane we need two points out of 10 points we can select 2 points in ${}^{10}{C}_2$ ways, but in this selection 4 points are through which only one line passes.
Hence total number of lines
${=}^{10}{C}_2{-}^4{C}_2+1$
Hence option (b)