Mastering the Combinations Problem: Buying a Dozen Donuts from 5 Types

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In summary, the conversation discusses the problem of determining the number of ways to buy a dozen donuts from 5 different types of donuts. It is determined that there are 5 possible combinations for 1 donut and 25 possible combinations for 2 donuts. However, there is a pattern where some combinations are repeated. After further discussion, it is concluded that the correct answer is 5^12.
  • #1
darthchocobo
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Can someone explain to me how to do this problem... I am really lost...

how many ways can you buy a dozen donuts from an unlimited supply of 5 types of donuts?
 
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  • #2
Ok there are 12 donuts you want , and 5 possible types of donuts.

so if you were to get only one donut, there would only be 5 possible combinations.

if you were to get 2 donuts, there would be 25 possible combinations...

11 12 13 14 15, 21 22 23 24 25, 31 32 33 34 35, 41 42 43 44 45, 51 52 53 54 55.

Now the problem there is some numbers are repeated. i.e 21=12, but according to your problem 21 and 12 are different ways (it does not say unique ways).

so 1 donut = 5, 2 donuts = 25. starting to see the patern?
 
  • #3
so the answer would be 5^12?
 
  • #4
Yes, that is correct.
 
  • #5
No, I don't think that's correct. Buying doughnut type 4 and doughnut type 5 is not different from buying type 5 and type 4.
 

FAQ: Mastering the Combinations Problem: Buying a Dozen Donuts from 5 Types

How many different combinations of donuts can be made from 5 types when buying a dozen?

There are 792 different combinations of donuts that can be made when buying a dozen from 5 types. This can be calculated using the formula nCr = n! / r!(n-r)!, where n is the number of types (5 in this case) and r is the number of items chosen (12 in this case).

Is it possible to buy a dozen donuts from 5 types without any repeats?

Yes, it is possible to buy a dozen donuts from 5 types without any repeats. This would be considered a permutation instead of a combination, and the number of possible permutations can be calculated using the formula nPr = n! / (n-r)!, where n is the number of types (5 in this case) and r is the number of items chosen (12 in this case).

Can I buy more than a dozen donuts from 5 types?

Yes, it is possible to buy more than a dozen donuts from 5 types. The number of possible combinations would increase with the number of donuts purchased. For example, if you wanted to buy 15 donuts, there would be 1,287 different combinations to choose from.

Can the same type of donut be chosen more than once in a combination?

Yes, the same type of donut can be chosen more than once in a combination. This allows for a larger variety of donut combinations to choose from.

Are there any limitations or constraints when solving the combinations problem for buying a dozen donuts from 5 types?

The only limitation or constraint when solving this problem is that the number of donuts chosen (12) must be less than or equal to the number of types (5). Otherwise, there would not be enough types of donuts to make a combination of 12.

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