Combinatorics/counting: How many configurations are possible for m differenct objects in n boxes of unlimited occupany (m<n)
Hello! The question is pretty much entirely in the title. I wasn't sure if I could just use the fundmental principle of counting here with m^n, as when I look up related formulae in statistical mechanics I get a different result.
Just to be clear:
Say there are 5 distinguishable objects and 20 distinguishable boxes. I can put up to 5 objects in a box. I am interested in how many different configurations, or states, are possible under these cirumstances.
What would change if the objects were indistinguishable?
I'm interested in a little supporting justification, just so I understand the answer. Thank you, geniuses!
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

4.8K
-
Please leave a comment if you need any clarifications.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1107 views
- $3.40
Related Questions
- Summation of Catalan Convolution
- Determine formula to calculate the radii of a unique ellipsoid from coordinates of non-coplanar locii on its surface, and without knowing its center or rotation angles.
- Logic Question 𝐴∧(𝐵∨𝐶)⊢(𝐴∧𝐵)∨(𝐴∧𝐶)
- Combinatorical Drawing
- Proof by induction the following recursive equation
- Estimating the Suit with 12 Cards: MLE and Confidence Intervals in a Figgie Starting Hand
- Discrete math- Range and preimage of the floor function
- Find the chromatic number of Kn, Kn,m, Cn.