There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

Question

There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines. (A) 106 (B) 105 (C) 60 (D) 55

Tardigrade Admin · Accepted Answer

Required number of lines = (number of lines made by 16 points) - (number of lines made by 6 collinear points) + 1 =16C2-6C2+1 =(16× 15/2× 1)-(6× 5/2× 1)+1 =120-15+1 =106

Q. There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

106

105

60

55

Required number of lines = (number of lines made by 16 points) - (number of lines made by 6 collinear points) + 1 $=^{16} C_{2} -^{6} C_{2} + 1$
$= \frac{16 \times 15}{2 \times 1} - \frac{6 \times 5}{2 \times 1} + 1$
$= 120 - 15 + 1$ $= 106$

Q. There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

106

105

60

55

Required number of lines = (number of lines made by 16 points) - (number of lines made by 6 collinear points) + 1 =16C2​−6C2​+1 =2×116×15​−2×16×5​+1 =120−15+1 =106

Required number of lines = (number of lines made by 16 points) - (number of lines made by 6 collinear points) + 1 $=^{16} C_{2} -^{6} C_{2} + 1$
$= \frac{16 \times 15}{2 \times 1} - \frac{6 \times 5}{2 \times 1} + 1$
$= 120 - 15 + 1$ $= 106$