Solving Stirling's Formula: 5000 Objects from 10000

[superwolf]

How many ways are there to choose 5000 objects out of a jar full of 10 000 distinct objects?

ATTEMPT:

Number of ways = (10000 5000)

ln 10000! = 10000 ln 10000 - 10 000 + 0.5ln(2*pi*M) = 82108 --> 10000! = e^82108

I still get overflow on my calculator!

 

[tiny-tim]

oooh … paper!

Hi superwolf!

ln 10000! = 10000 ln 10000 - 10 000 + 0.5ln(2*pi*M) = 82108 --> 10000! = e^82108

I still get overflow on my calculator!

then do it on paper first, putting in the 5000⁵⁰⁰⁰, do a bit of cancelling, and then worry the poor old computer!