A) \[{{{{(}^{m}}{{C}_{2}})}^{2}}\]
B) \[{{\left( ^{m+1}{{C}_{2}} \right)}^{2}}\]
C) \[{{\left( ^{m+2}{{C}_{2}} \right)}^{2}}\]
D) None of these
Correct Answer: C
Solution :
Each set is having \[m+2\] parallel lines and each parallelogram is formed by choosing two straight lines from the first set and two straight lines from the second set. Two straight lines from the first set can be chosen in \[^{m+2}{{C}_{2}}\] ways and two straight lines from the second set can be chosen in \[^{m+2}{{C}_{2}}\] ways. Hence the total number of parallelograms formed\[{{=}^{m+2}}{{C}_{2}}\ .{{\ }^{m+2}}{{C}_{2}}={{\left( ^{m+2}{{C}_{2}} \right)}^{2}}\].
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