1. Flip two coins. What is the multiplicity of the macrostate defined by getting one heads and one tails? What is the probability of getting this macrostate?

   multiplicity=2. Probability = multiplicity of 1 heads and 1 tails divided by the total multiplicity, so 2/4 = 1/2.

2. Flip 10 coins. What is the multiplicity of the macrostate with 9 heads?

   10. With 9 heads and 1 tails, the tails result could have been the 1st coin, 2nd coin, 3rd coin, etc, so there are 10 different ways to get the result.

3. What is the numerical value of ``6 choose 2''?

   6!/(2! 4!) = 720/(2*24) = 15

4. Suppose I flip a few hundred coins, and want to use the result as an analogy for a two-state paramagnet. How would I determine my system's energy by looking at the coins?

   The heads would be analogous to a spin aligned with the B field and tails a spin anti-aligned (or vice versa). So the ``energy'' would be determined by the difference between the number of heads and the number of tails.

5. Was there anything you had particular difficulty with in this reading? Is so, describe briefly.

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