0

I have a problem, how to distinguish between combinations and combinations with repetition.

Here is an example:

There are 10 different alcoholic drinks at the celebration. In how many different ways can I choose a drink for 15 people, so that every person drinks only one of the species?

My question is, how should I know, that I have to find combinations instead of combinations with repetition?

The answer to provided example is C(15 + 10 - 1) over (10 - 1)).

My solution was: Everyone can choose 1 drink from 15. Together it is 10*10*....10 = 10^15

mmmm93
  • 1
  • 1
  • 1
    Honestly? It depends on what you want! If you are asking in terms of how many different trays of drinks you can make where all you care about is how many of each drink is on the tray but don't care who took which drink, then you'd get the one answer. If it matters to you what drink the first guest received and what drink the second guest received, etc... then you'll get the other answer. Which is more correct? Really, neither. Which is more common to want to know about? The answer where each person's individual drink is relevant. – JMoravitz Dec 31 '19 at 13:44
  • That being said, you seem to have mixed two different problems., the one problem having the numbers $10$ and $15$, the other problem having the numbers $21$ and $9$. Please be more careful when writing a problem. – JMoravitz Dec 31 '19 at 13:45
  • I edited my solution, now it should be correct. I solved 2 examples at one time, sorry – mmmm93 Dec 31 '19 at 13:51
  • I suggest reading my answer to a related problem here discussing the question of whether when flipping two coins whether flipping a head then a tail should be considered the same or different than flipping a tail followed by a head. – JMoravitz Dec 31 '19 at 13:57
  • The question is a bit inaccurate, I agree. But that is the problem, I had to solve in school, so I can't do much with the question. – mmmm93 Dec 31 '19 at 13:59
  • JMoravitz thank you very much, I'll look up to the problem you posted here :) – mmmm93 Dec 31 '19 at 14:00
  • 2
    If it were in a test or homework setting, asking for clarification is generally encouraged. You can ask your teacher/proctor whether or not each individual person's drink order is relevant or whether it is merely the totals of the drinks which are relevant. You clearly are aware of the formulas for each, and hopefully understand which formula is used for which situation, which is all that should be being tested. You aren't being tested on your ability to read minds, but on your ability to perform math. – JMoravitz Dec 31 '19 at 14:01
  • Surely, I agree. Teacher gives us every lesson a list of examples we have to solve. But we do not solve all of them, because we do not have enough time. That's the one, that had to be too easy :) , so we moved on to more difficult problems. – mmmm93 Dec 31 '19 at 14:10

1 Answers1

1

There are 10 drinks. The first person has one choice, hence 10 drinks. For each such choice, the second one also has 10, hence 10×10. For 15 people it is $10^{15}$.

Alex
  • 19,262