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Let's say we think of a specific 12 letter word. How many times on average will that particular word appear in a string of 1 quintillion (10^18) completely random letters (i.e., uniform/equal probability for each letter A-Z at each position, with no preference for vowels or any other letter)?

Also, what will the actual frequency distribution look like? What would be the formula for that PDF (probability density function) distribution?

For simplicity, we should consider that each incidence is non-overlapping, as most words do not start with the sam letter(s) they end with.

Let's say we think of a specific $12$ letter word. How many times on average will that particular word appear in a string of $1$ quintillion ($10^{18}$) completely random letters (i.e., uniform/equal probability for each letter A-Z at each position, with no preference for vowels or any other letter)?

Also, what will the actual frequency distribution look like? What would be the formula for that PDF (probability density function) distribution?

For simplicity, we should consider that each incidence is non-overlapping, as most words do not start with the sam letter(s) they end with.