How to count occurrences of a word in all the files of a directory? But with count incremented only once per word per file

Question

This question is an additional constraint on this this question. I wanted achieve the word count by avoiding multiple counts for that same word in the same file? Eg : if word "aaa" appears in "file1.txt" 10 times, but count should increase only by 1 but not 10 & so on for other files too within a directory.

Answer 1

So what you want is the number of files that contain that word. Easy:

grep -l word *|wc -l