I’m confused when to use what (Permutation, Variations, Combinations)
@1.10 my understanding is to use variations without repetition as it does not consider order V569
I think you’ve got them mixed up. We use variations when “positions” and “order” matter, and combinations when they don’t. Below, I’m pasting you an answer to a previous question on distinguishing between the two:
Let’s start with the difference between the two and work through a simple example.
So, the main distinction between the two is that combinations don’t care about order, while variations do.
For instance, suppose you love tennis and you’re a big fan of Djokovic, Nadal and Federer. You know all 3 men were in the tournament and 2 of them reached the final. If you simply care which 2 made the final, but not who won, we would use combinations because order does not matter. Hence, if you only care about the match up, but don’t care who actually ends up as the victor, you use combinatorics -> C(3,2) = 3!/(2!*1!) = 3. The 3 combinations are, obviously, Djokovic vs Nadal, Nadel vs Federer or Djokovic vs Federer.
Now, if we care who lifts the trophy, we use variations because order is relevant. Then, we have V(3,2) = 3! / 1! = 6 ways they 3 competitors can arrange.
1) Djokovic 2) Nadal 3) Federer,
1) Nadal 2) Djokovic, 3) Federer
1) Djokovic 2) Federer 3) Nadal,
1) Nadal 2) Federer 3) Djokovic,
1) Federer 2) Nadal 3) Djokovic,
1) Federer 2) Djokovic, 3) Nadal
Thus, when some (or all) position matter, we are dealing with variations. For example, when we have to match banners to social media platforms in question 2, we have this artificial “order” because every position (platform) is different. The same distinction can be assigned to the tennis example, where we can name the positions: “winner”, “runner-up” and “not in final”. Essentially, as long as it matters who we put where, we have variations.
Hope this helps out and don’t hesitate to reach out if it doesn’t.
Hey Vik — I was overlooking this Q&A. And the variations formula in the example sentence I want to confirm is indeed the case. “Now, if we care who lifts the trophy, we use variations because order is relevant. Then, we have P(3,2) = 3! / 1! = 6 ways they 3 competitors can arrange.” The formula in respect to the tennis example is written as ” P(3,2) = 3! / 1! = 6.” Am I correct to assume this is to be written as “V(3,2) = 3! / 1! = 6”? Or what is the expression used for the “P” formula in this tennis example? P(n,p) = x! / (n-p)! –> (?)
Hey Bryan, sorry for the confusion, it should have been V(3,2), rather than P(3,2). You’re absolutely right, I’m going to edit my response. Best, 365 Vik