a$.$ A system with $4$ atoms can be in one of three macrostates which I will call I, II and III. The number of microstates for each macrostate are given in the table below.

$\backslash$table$[[$Macrostate$,$Number of Microstates$],[$I$,2],[$II$,3],[$III$,5]]$

What fraction of the time will you see the system in macrostate III?

A$.100\%$

B$.3\%$

C$.2\%$

D$.50\%$

E$.5\%$

F$.33\mathrm{.}3\%$

G$.75\%$

H$.10\%$

I. $20\%$

b$.$ As the number of particles increases, what would you expect to happen?

Select all of the options which are likely to be true.

A$.$ The probability of macrostate II will likely go down.

B$.$ The probability of macrostate III will likely go down.

C$.$ The probability of macrostate III will likely go up$.$

D$.$ The probability of macrostate I will likely go down.

E$.$ The probability of macrostate I will likely go up$.$

F$.$ The probability of macrostate II will likely remain the same.

G$.$ The probability of macrostate II will likely go up$.$

H$.$ The probability of macrostate III will likely remain the same.

I. The probability of macrostate I will likely remain the same