Use Stirling's approximation to calculate the second column from the given table.

Table 6-1 Multiplicities of Selected States for an N-molecule Monatomic Gas N Ratio 10 S2(N, N/2) 252 1.0 x 1029 2.7 x 10299 S2(N, N/2 + 0.10N) 210 1.4 x 1028 5.0 x 10290 100 0.83 0.14 2 x 10-9 1000 Note: The ratio in the final column is the ratio of the two preced- ing columns, showing the relative likelihood of a 10% deviation from the peak value. Table 6-1 Multiplicities of Selected States for an N-molecule Monatomic Gas N Ratio 10 S2(N, N/2) 252 1.0 x 1029 2.7 x 10299 S2(N, N/2 + 0.10N) 210 1.4 x 1028 5.0 x 10290 100 0.83 0.14 2 x 10-9 1000 Note: The ratio in the final column is the ratio of the two preced- ing columns, showing the relative likelihood of a 10% deviation from the peak value