How do i find permutation of a word containing a certain word?

Question

We can assume the word has all unique characters. For example, ABC's permutations are ABC, ACB, BAC, BCA, CAB, CBA. How would I find the number of permutations of ABC containing for example, AB? What is its relation to the original word?

Answer 1

If you want to know how many times the substring AB appears in the set of all permutations of the string ABC, simply consider AB as a whole (as if it was a single letter). So instead of 3!, it would be 2! = 2 times.

For example, if you have 3 boxes A, B, C and you want to generate all the permutations of the boxes where the box B is immediately after the box A, then you simply drag A and B at the same time, as if they were a single box. That's the reasoning.