I'm having a lot of trouble deciding when to call an object in a problem a Ball vs an Urn (a box). Once that's decided, I'm then unsure when to call each of them labelled vs unlabelled.
Current understanding and thought process
My current understanding is one ball can only go into one urn. An urn cannot go into a ball.
When deciding if an object is a ball vs an urn, I ask myself: Does it make literal sense to put X into Y. If it does, I call X the ball and Y the urn.
Then when I decide if a ball or urn is labelled vs unlabelled, I ask myself: Can we distinguish one object from another? If yes, it's labelled.
Some example problems
- Knowing that from 10 people we can choose a committee in 210 different ways, in how many ways can we chose the same committee if we have 12 people?
- Consider that you have a bowl of generic fruits (different amounts of the same fruit do not make a difference). How many different fruit salads can you make using a certain amount of ingredients per salad (a certain number of fruits that you are to put in each salad), if you know that excluding a fruit from the initial bowl will give you 1330 ways of making fruit salads each with as many ingredients, while excluding a fruit and using an ingredient less, will give you 5985 different fruit salads.
Questions vs thought process
The first question I first struggled with identifying whether a committee position was distinguishable from others? (are the roles different e.g. the president vs secretary)
The second question says that the fruit bowl could contain more than one of the same fruit so they're indistinguishable meaning something is unlabelled. I'm guessing the bowls here are the other object in the question. To find out which is the ball vs the urn, I ask 'Does it make literal sense to put fruit into fruit bowls'. It does, so I consider the fruit to be balls and the urns to be the fruit bowls. The balls are unlabelled, the urns I'm still not sure here but I guessed unlabelled because how can we tell one bowl from another? Also, to classify as a fruit salad each bowl must have at least one piece of fruit. Therefore I'd say the question is unlabelled balls, unlabelled urns and more than one ball per urn but apparently the question is unlabelled balls, labelled urns and more than one ball per urn.
Could someone help improve questions I can ask myself to understand the question in terms of balls vs urns and labelled vs unlabelled or help guide me?