Number of ways to convert a string to another

Finding number of ways to convert a string to another with only 2 kinds of operations:

-delete a character

-change position of character

eg-accb to acb. There are 2 ways to remove a ‘c’ to get the result.

Means you want to convert a given string to a string that will not contain any repeated character. Am I right?

no. take this example:
abccd to abcc. there is only 1 way by deleting a d.
current string and target strings are inputs.

This is the well known edit distance problem. Learn from here.

This a standard problem statement of transforming a string to another string by either deleting a character or swapping characters of a string in c.

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