Number of substrings - Combinatorics

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Say you have two strings $A = a$ and $B = b$. Now, how do I come up with an expression that gives me the number of substrings of $C = abaa$ that contain atleast one occurrence of both $A$ and $B$?

The number of substrings of $C$ that contain both $A$ and $B$ are:

$ab$

$ba$

$baa$

$aba$

$abaa$

How do I model this in combinatorics?