Stirling's formula probability

[indigojoker]

Use Stirling's formula, n!=sqrt(2 pi n) n^n e^{-n}, to estimate the probability that all 50 states are represneted in a group of 50 councilmen chosen at random.

I think it should be:

P=\frac{50!}{50^{50}}

So using Stirling's formula, we get:

P=\frac{\sqrt{2 \pi 50} 50^{50} e^{-50}}{50^{50}}
P=\sqrt{2 \pi 50} e^{-50}

is this the correct approach?

 

[Unco]

Use Stirling's formula, n!=sqrt(2 pi n) n^n e^{-n}, to estimate the probability that all 50 states are represneted in a group of 50 councilmen chosen at random.

I think it should be:

P=\frac{50!}{50^{50}}

So using Stirling's formula, we get:

P=\frac{\sqrt{2 \pi 50} 50^{50} e^{-50}}{50^{50}}
P=\sqrt{2 \pi 50} e^{-50}

is this the correct approach?

Presuming each councilman represents one of the 50 states, your work is correct!