Imagine there is an alphabet a that contains |a| characters to choose from. Furthermore, there is a word w that consists of |w| characters of said alphabet (such a word is just a random combination of characters, it doesn't need to have a real meaning in a natural language).
I'm wondering how many possibilities there are to exchange exactly n characters of a particular, given word with other characters from the alphabet (there are |a|-1 characters to choose from when replacing each character since a character should not be replaced with itself).
Example:
a = { A, B, C, D }
w = BCADDBACADCBAA
n = 3
So the goal is to find out the total amount of variations of w that differ in exactly 3 places.
My math background is not very strong, but I came up with the following naive approach:
- The number of ways (let's call it "iterations") to choose n characters from w to replace is
- In every iteration, each of the n characters can be replaced with one of |a|-1 characters, which leads to
possibilities
So isn't the amount of total variations just the following?