Still is not clear when should I use combination with repetition and its difference with variation with repetition. Could please help me with some example and extra exercises? Thanks a lot for your time and attention.
Here is a response to a similar question explaining the difference between combinations and variations (w/o repetition):
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.
Now, as for the difference between the two when it comes to repetition, think of it this way – does it make a difference when we pick what? If no – we’re using combinations, if yes – we’re using variations. Once again, this all comes down to this artificial order, where the different positions matter. Hence, if we have to select what 3 flavors of ice cream to get for our Sundae, we’d use combinations with repetition, but if we’re talking about different ways to repaint the house, then we’re using variations (because it matters what color each room is).
Hope this helps out and don’t hesitate to reach out if it doesn’t.
“does it make a difference when we pick what”. Could not understand meaning of this statement. Please elaborate last paragraph.
you can explain the same example with repetition
Hey Chintan, the idea is that if we’re selecting something with repetition, the distinction between variations and combinations is a bit harder to find. So, if it matters when we’re selecting one of the elements (as in first, second, third, etc), then we’re dealing with variations. If not, we’re dealing with combinations. For example, if we’re picking the toppings to put on a pizza, it doesn’t matter if we put onions first, and then pepperoni, or pepperoni first, and onions second. Hence, we would use combinations in that case. However, if we’re very organized and like to pick our outfits for the week in advance, it makes a difference whether we wear the white shirt and blue pants on Monday, and the blue shirt and navy blue pants on Tuesday, or vice versa. The idea with variations is that the order (in this case – days of the week) increases the number of ways we can conduct the task (organize our wardrobe). Sorry for the delayed response and I hope this helps!
When it comes to order/position use variation else Combination to be used