I think there are 2 mistakes here. First you are missing an n!. There are only ~ 10,000 skill pairs if (physics , writing) is different from (writing , physics). There are ~ 5,000 unordered pairs.
Secondly is the assumption that no one else can have more skills than you. If everyone picks 5 skills to get good at, you can be the only person in the world with that combo of skills. If you get to pick 5 skills. And some other people are good at all 100, you don’t get a unique combo. If 32 people each have 50 skills, then you probably don’t have a unique combo.
Thank you for the correction. Adding the missing factorial increases the answer from five to six.
You don’t need a unique combination. You just need combination nobody else is competing at. If someone has more skills than you then there is a combinatorial explosion in the possibility space available to zem. The odds zir work collides with yours goes down fast as the number of skills your superior has goes up. Ze likely have better things to do than compete with you.
I think there are 2 mistakes here. First you are missing an n!. There are only ~ 10,000 skill pairs if (physics , writing) is different from (writing , physics). There are ~ 5,000 unordered pairs.
Secondly is the assumption that no one else can have more skills than you. If everyone picks 5 skills to get good at, you can be the only person in the world with that combo of skills. If you get to pick 5 skills. And some other people are good at all 100, you don’t get a unique combo. If 32 people each have 50 skills, then you probably don’t have a unique combo.
Thank you for the correction. Adding the missing factorial increases the answer from five to six.
You don’t need a unique combination. You just need combination nobody else is competing at. If someone has more skills than you then there is a combinatorial explosion in the possibility space available to zem. The odds zir work collides with yours goes down fast as the number of skills your superior has goes up. Ze likely have better things to do than compete with you.