How many parallelograms are there in the given figure?
![Screenshot 2025-04-07 011910.png](https://res.cloudinary.com/aptidude/image/upload/v1743969169/aptidude_questions/lqgzi66drenq4gkkkkbm.png)

Question

How many parallelograms are there in the given figure? 
![Screenshot 2025-04-07 011910.png](https://res.cloudinary.com/aptidude/image/upload/v1743969169/aptidude_questions/lqgzi66drenq4gkkkkbm.png)

Accepted Answer

To determine the total number of parallelograms in the given figure, we count all possible parallelograms formed by intersecting lines. The calculation involves summing up the parallelograms formed by different combinations of rows and columns.

### Step-by-step solution:  
1. Count the parallelograms formed by selecting two rows and two columns:  
   - For rows: There are $$4$$ rows, and the number of ways to select two rows is $$ \binom{3}{2} = 3 $$.  
   - For columns: There are $$5$$ columns, and the number of ways to select two columns is $$ \binom{5}{2} = 10 $$.

2. Multiply these combinations to get the total number of parallelograms:  
   $$ 	ext{Total parallelograms} = 3 	imes 10 = 30. $$

Thus, the total number of parallelograms in the figure is **30**, corresponding to option **(b)**.

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