Construct a table of all the possible combinations of numbers that can come up when you throw two dice. Your friend says, “Yes, I know that 7 is the most likely total number when two dice are thrown. But ?why 7?” Based on your table, answer your friend, and explain that, in thermodynamics, the situations that are likely to be observed are those that can be formed in the greatest number of ways.

Solution 8P The following table contain all the possible combination of number that can come up when we throw two dice. 1 1 4 1 1 2 4 2 1 3 4 3 1 4 4 4 1 5 4 5 1 6 4 6 2 1 5 1 2 2 5 2 2 3 5 3 2 4 5 4 2 5 5 5 2 6 5 6 3 1 6 1 3 2 6 2 3 3 6 3 3 4 6 4 3 5 6 5 3 6 6 6 Let us now make a table all the possible combination of a particular number of outcome. Outcome Possible combinations Total number of possible outcome 2 (1+1) 1 3 (1+2), (2+1) 2 4 (1+3), (2+2), (3+1) 3 5 (1+4), (2+3), (3+2), (4+1) 4 6 (1+5), (2+4), (3+3), (4+2), (5+1) 5 7 (1+6), (2+5), (3+4), (4+3), (5+2), (6+1) 6 8 (2+6), (3+5), (4+4), (6+2), (5+3) 5 9 (3+6), (4+5), (5+4), (6+3) 4 10 (4+6), (5+5), (6+4) 3 11 (5+6), (6+5) 2 12 (6+6) 1 From the table, we can see that there are 6 possible ways to form the outcome as 7. This is the maximum number of ways that a particular out come can be formed by throwing two dice. Hence the probability of the outcome of 7 is maximum. The situation is similar to the thermodynamics also. In thermodynamics also, there are lots of different ways by which an ensemble can be formed. But the probability of having a particular combination is maximum if the number of ways that particular combination can be achieved is maximum.