There are two boxes containing five balls each. The balls are labeled from 1 to 5. One ball is drawn from each box. How many ways can the drawn balls get a sum of 4? Determine the most probable total.

Four boxes (1, 2, 3, and 4) of equal volume are distributed with ideal gas molecules. In how many ways can the following states be attained? Determine the entropy for each state using Boltzmann's equation. 

(i) 3 molecules in box 1 

(ii) 3 molecules randomly distributed among boxes 1, 2, 3, and 4

The entropy of a system decreases as it goes to state B from state A. Will its number of microstates increase or decrease?

Differentiate a microstate of a system from a state of a system

There are two possible ways to roll a 3 using two dice each numbered 1-6. Therefore, there are two microstates for the outcome of 3 (a specific microstate). Determine the number of possible ways to roll a 4. Calculate the entropy associated with an outcome of 4. (K_B = 1.38×10^–23)