Question

Find the number of ways of putting 2 particles in 5 boxes according to the different kinds of statistics.

Short answer

The solution is derived as mentioned below.

$\begin{array}{l}{\text{M}}_{\text{1}}\text{=25}\\ {\text{M}}_2\text{=10}\\ {\text{M}}_3\text{=15}\end{array}$

Step-by-step solution

Given Information.

Number of particles is 2 and number of boxes is 5.

Definition of Probability.

Probability means the chances of any event to occur is called it probability.

 Step 3: Find the probability

Use Maxwell-Boltzmann: In this model particles are distinguishable so the number of method can be arranged $\text{N}=2$particles in $\text{n}=5$boxes using this method.

$\begin{array}{c}{M}_1=n^N\\ =5^2\\ =25\end{array}$

Use Fermi-Dirac: In this model particles are not distinguishable so the number of method can be arranged $\text{N}=2$particles in$n=5$using this method.

$\begin{array}{c}{\text{M}}_{\text{2}}\text{=C(n,N)}\\ \text{=C(5,2)}\\ \text{=10}\end{array}$

Use Bose-Einstein: In this model particles are not distinguishable as in Fermi-Dirac but the difference here is that's allowed to put two balls in same box so the number of method can be arrangeddata-custom-editor="chemistry" $\text{N}=2$particles in$n=5$boxes using this method.

$\begin{array}{c}{\text{M}}_{\text{3}}\text{=C(n-1+N,N)}\\ \text{=C(6,2)}\\ \text{=15}\end{array}$

Hence, the solution is mentioned below.

$\begin{array}{l}{\text{M}}_{\text{1}}\text{=25}\\ {\text{M}}_2\text{=10}\\ {\text{M}}_3\text{=15}\end{array}$