Combinatorics Problem: How Many Ways Can I Put K Birds into M Cages?

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Homework Help Overview

The problem involves determining the number of ways to distribute K labeled birds into M labeled cages, with no restrictions on the number of birds per cage and the possibility of empty cages.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the labeling of both birds and cages, which influences the counting method. One participant suggests a method involving assigning labels to the birds, while another hints at a straightforward solution based on this labeling.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem based on the labeling of birds and cages. Some guidance has been offered regarding the counting approach, but no consensus has been reached on the final solution.

Contextual Notes

The original poster mentions a lack of background in combinatorics, which may affect their understanding of the problem. There is also a note about the absence of specific combinatorial principles being applied in the discussion.

iamalexalright
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Homework Statement


I have K birds to put into M cages. How many ways can I do this(no limit on the amount of birds in a cage - there can be empty cages)?


Unfortunately I haven't had a combinatorics course (and my friends who have apparently have forgotten all of it...) so I'm a little lost.

A push in the right direction would be most appreciated.
 
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Are the cages numbered/labeled?
Are the birds numbered/labeled?
 
Both the birds and the cages are labeled
 
hi alex! :smile:

if the birds are all distinguishable, you just line them up, put a letter from 1 to M round their necks, and read off the overall number …

how many different overall numbers are there? :wink:
 
well, in that case the answer is really trivial and straightforward. Give it another try.
 

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