If m parallel lines in a plane are intersected by a family of n parallel lines, then the number of parallelograms that can be formed is

Question

If m parallel lines in a plane are intersected by a family of n parallel lines, then the number of parallelograms that can be formed is (A)  (1/4)mn(m-1)(n-1)  (B)  (1/2)mn(m-1)(n-1)  (C)  (1/4)m2n2  (D) None of these

Tardigrade Admin · Accepted Answer

Selection of 2 parallel lines from m= m C2 Selection of 2 parallel lines from n= n C2 Hence, number of parallelograms = m C 2 ⋅ n C 2 =(1/4)(m-1)(n-1) m n

Q. If $m$ parallel lines in a plane are intersected by a family of $n$ parallel lines, then the number of parallelograms that can be formed is

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

$\frac{1}{2} mn (m - 1) (n - 1)$

$\frac{1}{4} m^{2} n^{2}$

None of these

Selection of $2$ parallel lines from $m =^{m} C_{2}$
Selection of $2$ parallel lines from $n =^{n} C_{2}$
Hence, number of parallelograms $=^{m} C_{2} \cdot^{n} C_{2}$
$= \frac{1}{4} (m - 1) (n - 1) mn$

Q. If m parallel lines in a plane are intersected by a family of n parallel lines, then the number of parallelograms that can be formed is

41​mn(m−1)(n−1)

21​mn(m−1)(n−1)

41​m2n2