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

[darthchocobo]

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?

 

[SNOOTCHIEBOOCHEE]

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?

 

[darthchocobo]

so the answer would be 5^12?

 

[SNOOTCHIEBOOCHEE]

Yes, that is correct.

 

[AKG]

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.