Inspired by my struggles with this puzzle.
In that puzzle, I needed to mix two words, meaning blend them together without changing the order. For example, "ab" mixed with "cd" would give us 6 new words: 'abcd', 'acbd', 'acdb', 'cabd', 'cadb', 'cdab'.
Now, if we have a common letter, there would be repeated words, and we want to eliminate those. For example, "ab" mixed with "acd" would give us 7 words: 'aabcd', 'aacbd', 'aacdb', 'abacd', 'acabd', 'acadb', 'acdab'.
This got me thinking about the combinatorics problem: How would we work out that "ab" and "acd" has 7 mixtures without just listing them out and counting them?
So the puzzle is this:
1. Calculate "by hand" the number of mixtures of "evince" and "decor".
2. Explain the methodology you used. There is a neat tweak on a standard method that gets the answer out.
Note: "By hand" doesn't literally need to be by hand. What I'm looking for is any non-brute-force method, ie doesn't involve listing them out and counting them.