Count number of subarrays containing an element
Let’s say we have an array [1, 2, 3, 4],
count the number of subsequences containing element 3.
The formula is (i + 1) * (N - i).
On the left of element 3 (inclusive of 3), you have [1], [1, 2], and [1, 2, 3], which are three subsequences.
On the right of element 3, you have [] (empty subsequence) and [4], which are two subsequences.
Multiplying the choices on the left and the right gives the total count: 3 * 2 = 6.