Number of parallelograms when n horizontal parallel lines intersect m vertical parallel lines

Given two positive integers n and m. The task is to count number of parallelogram that can be formed of any size when n horizontal parallel lines intersect with m vertical parallel lines. 

👁 Image

Examples: 

Input : n = 3, m = 2
Output : 3
2 parallelograms of size 1x1 and 1 parallelogram 
of size 2x1.
Input : n = 5, m = 5
Output : 100

The idea is to use Combination, which state, number of ways to choose k items from given n items is given by ⁿC_r. 
To form a parallelogram, we need two horizontal parallel lines and two vertical parallel lines. So, number of ways to choose two horizontal parallel lines are ⁿC₂ and number of ways to choose two vertical parallel lines are ^mC₂. So, total number of possible parallelogram will be ⁿC₂ x ^mC₂.
Below is C++ implementation of this approach: 

100

Time Complexity: O(n²) 
Auxiliary Space: O(n²)

Approach: Using Basic Maths

The same Question can be Solved By just using the basic maths
as we know ⁿC₂ = n*(n-1)/2 and same for ^mC₂ so just using basic maths we can solve the question in O(1)

Below is the implementation of the above approach:

100

Time Complexity :O(1)
Space Complexity : O(1)
This article is contributed by Aarti_Rathi and Dhruv Khoradiya.