[QUE/SM-03012] SM-PROBLEM

 Consider a container of volume V with N non interacting particles. Consider a small volume $v$ inside it. Making the assumption that the particles have equal probability to be anywhere inside the container find the probability $P(n)$ of the volume $v$ containing $n$ particles. Maximize the expression and show that the most probable value is $\frac{N}{V}v$. Find the width of the distribution. If $N\,=\,10^{22}$ , what is the width of the distribution. If the deviation of the density should be less that $1$ percent what should be the volume $v$?

HSMani