For a toss of 100 coins, Table 15.4 gives the number of microstates for each macrostate, with a grand total of 1.27 x 10^30 microstates across all macrostates. How many of those microstates correspond to the macrostate of exactly 50 heads and 50 tails, the most disorderly and most likely outcome?

1. Table 15.4 lists the number of microstates, W, corresponding to each possible macrostate of 100 coin tosses. 2. The most orderly macrostates, 100 heads or 0 heads, correspond to only 1 microstate each, while the most disorderly macrostate, 50 heads and 50 tails, corresponds to a vastly larger count. 3. This count is stated directly: there are 1.0 x 10^29 ways to get 50 heads and 50 tails, the least orderly arrangement. 4. Option D, 1.27 x 10^30, is instead the grand total across every possible macrostate, not the count for 50 heads and 50 tails alone. 5. Options A and C, 1.7 x 10^13 and 2.4 x 10^23, correspond to other rows of the table rather than to the 50-50 row. 6. Checking scale confirms the choice: 1.0 x 10^29 is comfortably smaller than the 1.27 x 10^30 grand total but vastly larger than the single-microstate counts for the most orderly macrostates, exactly as expected for the single most probable row in the table. _Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation_