With two dice, each numbered 1-6, there are two possible ways to roll a 3: thus, for the outcome of 3 (a particular macrostate) there are 2 microstates. how many possible ways are there to roll a 6?

what is the entropy associated with an outcome of 6?
s=?

Possible number of ways to a roll 6=5

Explanation:

We are given that two dice are rolled.

There are two possible ways to roll 3:(1,2) and (2,1).

For the outcome of 3 (a particular macrostate) there are 2 microstates.

We  have to find the possible  number of ways to roll a 6.

We have to find the entropy associated with an outcome of 6.

Possible number of ways to roll 6=(1,5),(5,1),(2,4),(4,2),(3,3)=5

Therefore, possible number of ways to roll 6=5

Entropy associated with an outcome of 6=

w=Number of ways

Substitute the value

S=

Hence, the entropy associated with an outcome of 6=