A) \[\frac{1}{4}mn(m-1)(n-1)\]
B) \[\frac{1}{2}mn(m-1)(n-1)\]
C) \[\frac{1}{4}{{m}^{2}}{{n}^{2}}\]
D) None of these
Correct Answer: A
Solution :
Selection of 2 parallel lines from\[m{{=}^{m}}{{C}_{2}}\] Selection of 2 parallel lines from\[n{{=}^{n}}{{C}_{2}}\] Hence, number of parallelograms\[{{=}^{m}}{{C}_{2}}{{\cdot }^{n}}{{C}_{2}}\] \[=\frac{1}{4}(m-1)(n-1)mn\]
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