help! (1 Viewer)

[nike33]

600! / (300! x 300! x 2^600) can someone pls give me an approx to this (a few sig figures) or a site with a large calculator...thanks!

 

[Calculon]

0.032559931334979678350422392588404...
From windows caculator

 

[nike33]

thanks!

 

[CM_Tutor]

Nike33, if you want to estimate things like this, Stirling's approximation to n! can be useful. It is:

n! ~ sqrt(2 * pi) * n^n+0.5 / eⁿ.

Using this result, 600! / (300! x 300! x 2⁶⁰⁰) is approximately 1 / sqrt(300 * pi)

Furthermore, using the method of 1995 4u HSC, question 7,
1 / sqrt(300.5 * pi) < 600! / (300! x 300! x 2⁶⁰⁰) < 1 / sqrt(300 * pi)

 

[nike33]

a qn7/8 binomial inequality for our hsc qn7/8 would be cool...got any laying around i can have a go at CM /..happy bday btw