If m points on one straight line are joined to n points on another straight line. The number of points of intersection of the line segments thus formed is

Question

If m points on one straight line are joined to n points on another straight line. The number of points of intersection of the line segments thus formed is (A) (mC2 ⋅ nC2/4) (B) (mn (m-1)(n-1)/4) (C) (mC2 ⋅ nC2/2) (D) mC2 + nC2

Tardigrade Admin · Accepted Answer

Each selection of 4 points, two on one line and two on the other will give one point of intersection as desired in the question. ∴ Required number = mC2 ⋅ nC2 =(mn (m-1)(n-1)/4)

Q. If $m$ points on one straight line are joined to $n$ points on another straight line. The number of points of intersection of the line segments thus formed is

$\frac{^{m} C _{2} \cdot ^{n} C _{2}}{4}$

$\frac{mn ( m - 1 ) ( n - 1 )}{4}$

$\frac{^{m} C _{2} \cdot ^{n} C _{2}}{2}$

$^{m} C_{2} +^{n} C_{2}$

Each selection of $4$ points, two on one line and two on the other will give one point of intersection as desired in the question.
$∴$ Required number
$=^{m} C_{2} \cdot^{n} C_{2}$
$= \frac{mn ( m - 1 ) ( n - 1 )}{4}$

Q. If m points on one straight line are joined to n points on another straight line. The number of points of intersection of the line segments thus formed is

4mC2​⋅nC2​​

4mn(m−1)(n−1)​

2mC2​⋅nC2​​

mC2​+nC2​