Practice: The macrostate of a set of coins is given by the number of coins that are heads-up. If you have 100 coins, initially with 20 heads-up, what is Δ𝑆 when the system is changed to have 50 heads-up? Note that the multiplicity of k coins which are heads-up, out of N total coins, is Ω = 𝑁!/𝑘!(𝑁−𝑘)! . Does this change in macrostate satisfy the second law of thermodynamics?