Call placement of a particle in box A$,$heads$$ and placement in box B$,$tails$.$ Given one particle, there are two ways of arranging it$,$ H or T$.$ For two particles, there are four ways of arranging them, $\{$HH$,$HT$,$TH$,$TT$\}.$We can treat the microstates by considering each particle in order. For example, $\{$H T H H$\}$ means the first particle is in box A$,$ the second in box B$,$the third in box A$,$ and the fourth in box A$.$

Use Stirling$$s approximation to estimate the change of entropy in going from a distribution of $50\mathrm{.}1\%$ of $6\mathrm{.}022$E$23$ in box A to a distribution of $50\mathrm{.}001\%,$ and from $50\mathrm{.}001\%$

to $50\mathrm{.}000\%.($ANS$.1\mathrm{.}2$E$18$ J$/$K$)$