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Permutations vs Variations vs Combinations

Permutations vs Variations vs Combinations

Super Learner
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Hi,
I have understood the concept of Permutations, Variations, and Combinations, but I find it hard to distinguish them in the exercises  

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365 Team
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Hey Ahmed, 
So, Permutations are when we arrange the entire set. You can think of them as a special case of Variations where n = p and just distinguish between using variations and combinations. As for the difference 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 P(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.
Best,
365 Vik

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