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!