Question

Find the number of ways of putting$2$particles in$4$boxes according to the three kinds of statistics.

Short answer

The required values are mentioned below.

$\begin{array}{c}M=16\\ M=6\\ M=10\end{array}$

Step-by-step solution

Given Information.

The two particles are in four boxes.

Definition of uniform sample spaces.

If a given experiment's sample space is known to be uniform, the probability of an event can be calculated using the event sizes and the sample space.

Find the methods

The formula for Maxwell-Boltzmann states that $M=n^N$.

$\begin{array}{c}M=4^2\\ =16\end{array}$

Use Fermi-Dirac method.

$\begin{array}{c}M=C(N,n)\\ =C(4,2)\\ =6\end{array}$

Use Bose Einstein method.

$\begin{array}{c}M=C(n-1+N,n)\\ =C(5,2)\\ =10\end{array}$

Hence, the required valuesare given below.

$\begin{array}{c}M=16\\ M=6\\ M=10\end{array}$