Combination locks are quite common in our lives. As I was taking a shower one day, I thought to myself: Why are combination locks named combination locks, but not permutation locks? Let me first explain the difference between combination and permutation.

Combination refers to a selection of items such that its order does not matter. A (hopefully easily-understandable) example would be a basket of fruit holding 3 apples and 2 oranges. Let's say we want to pick 2 fruits from this basket. If we do so, we can get:

• 2 apples; or
• 2 oranges; or
• 1 apple and orange each

What I want to emphasize, however, is the fact that the order of selection does not matter. Whether we get an apple or an orange first, if we end up with one of each, to us it's the same. This also applies to the other outcomes. Let's say I marked the apples and oranges. If we get 2 apples, we could get apple number 1 first, then apple number 2, or some other order. In the end, it doesn't matter though since we only care that we got 2 apples. As long as the result contains the same items (same amount per type), they can be considered as the same combination.

What about permutation? This may be a word you're not familiar with if you don't know many mathematics. Permutations are very similar to combinations, except there's a clear difference: the ordering matters. An example I like to use is the spelling of English words. Let's say you're given the letters 'a', 'e' and 't'. You can spell different words with them, for instance, the words "ate", "eat" and "tea". If this becomes a bag of letters, you would think pulling out 'e', 'a', 't' and 't', 'e', 'a' (in their listed order) are different scenarios. If we apply the concept of combination to them, then this would be untrue, as they're essentially the same as getting an apple, orange and pear out of a fruit basket of many fruits. However, in the concept of permutations, they are different as the order of the letters is different.

Going back to combination locks, we all know that 123 and 321 are different passwords, as you cannot unlock a combination lock with password 123 using 321. That is why, in my mind, combination locks should be called permutation locks. The lock depends on a list of permutations. If the locks use combinations, then the security of these locks would be significantly lower.

Will I start calling combination locks permutation locks now? No, not really. In English convention, people still refer to them as combination locks. I doubt if most people would know/remember what permutation means, and what I would be referring to if I utter the words "permutation lock" without prior context in a normal conversation.

Anyhow, this is just me writing down a shower thought that occurred randomly. I hope you didn't find this detrimental to your brain cells.