- #1
Demroz
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Homework Statement
The stirling approximation, J! = √JJ+1/2e-J, is very handy when dealing with numbers larger than about 100. consider the following ratio: the number of ways N particles can be evenly divided between two halves of a room to the number of ways they can be divided with 60% on the right and 40% on the left.
a. Show using the stirling approximation that the ratio is approximately (0.40.40.60.6/5)n
Homework Equations
N!/NR!(N - NR)!
J! = √JJ+1/2e-J
The Attempt at a Solution
So i figured out the ratio to be
(0.5n)!(0.4n)!/(0.5n)!
Then by using the stirling approximation I get
0.6n0.6n+1/20.4n0.4n+1/2 / 0.25nn+1
all of my attempts so far have given me that answer which simplifies to 24/25. can you guys point me in the right direction/show me what I'm doing wrong?