Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are

Question

Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are (A)  18 C2- 5 C2+1 (B)  18 C2- 5 C2 (C)  18 C 2- 4 C 2 (D) None of these

Tardigrade Admin · Accepted Answer

Number of lines that can be formed on joining 18 non-collinear points

=^{18} C_{2}

Number of lines formed by joining 5 collinear points is only 1.
Number of lines if the 5 points have been non-collinear

=^{5} C_{2}

Required number of lines

=^{18} C_{2} -^{5} C_{2} + 1

Q. Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are

$^{18} C_{2} -^{5} C_{2} + 1$

$^{18} C_{2} -^{5} C_{2}$

$^{18} C_{2} -^{4} C_{2}$

None of these

Number of lines that can be formed on joining 18 non-collinear points $=^{18} C_{2}$
Number of lines formed by joining 5 collinear points is only 1.
Number of lines if the 5 points have been non-collinear
$=^{5} C_{2}$
Required number of lines $=^{18} C_{2} -^{5} C_{2} + 1$

Q. Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are

18C2​−5C2​+1

18C2​−5C2​

18C2​−4C2​

None of these

Number of lines that can be formed on joining 18 non-collinear points =18C2​ Number of lines formed by joining 5 collinear points is only 1. Number of lines if the 5 points have been non-collinear =5C2​ Required number of lines =18C2​−5C2​+1

$^{18} C_{2} -^{5} C_{2} + 1$

$^{18} C_{2} -^{5} C_{2}$

$^{18} C_{2} -^{4} C_{2}$

Number of lines that can be formed on joining 18 non-collinear points $=^{18} C_{2}$
Number of lines formed by joining 5 collinear points is only 1.
Number of lines if the 5 points have been non-collinear
$=^{5} C_{2}$
Required number of lines $=^{18} C_{2} -^{5} C_{2} + 1$