- #1

- 191

- 0

## Homework Statement

I don't really understand how to use Stirling's approximation. here's an example

you flip 1000 coins, whts the probability of getting exactly 500 head and 500tails

## Homework Equations

N!=N

^{N}e

^{-N}(2pieN)

^{1/2}

## The Attempt at a Solution

wht they did was

2

^{1000}total number outcome

[tex]\Omega[/tex](500)=1000!/500!

^{2}multiplicity

than used the Stirling's approximation to get this which I don't get how. What do I plug in for N

[tex]\Omega[/tex](500)=2

^{1000}/(500pie)

^{1/2}

P=[tex]\Omega[/tex](500)/2

^{1000}= 1/(500pie)

^{1/2}= .025

thanks