A collection of 800 indistiguishable coins lie on a table, 720 are heads up and the rest are tails up. The table is violently shook causing many of the coins to flip. Afterward 370 are heads up and the rest are tails up. Compute the quantity Delta lnW for this situation

Answer 1

If n1 are heads up and n2 are tails up, then W = (n1 + n2)!/[(n1)!(n2)!]

Delta Log(W) is thus given by:

Delta Log(W) =

log(720!) + log(80!)-log(370!)- log(430!)

You can simplify this using Stirling's approximation:

log(n!) = n log(n) - n

Answer 2

Thank you very much