How to calculate 200C65 (for binomial distribution formula)

[socrates_1]

Hi, I have tried to calculate 200C65 on my calculator but the calculator gives an error. Do u know how to do it?
I also tried to calculate it through the formula with the ! but doesn't give an answer.

 

[mathman]

Hi, I have tried to calculate 200C65 on my calculator but the calculator gives an error. Do u know how to do it?
I also tried to calculate it through the formula with the ! but doesn't give an answer.

I don't know the limit on number size for your calculator, but the simplest brute force solution would be:
(200/65)(199/64)...(136/1)

 

[Ibix]

Stirling's formula is a way of approximating large factorials.

Mathman's approach is easy and exact if you have a computer or programmable calculator, but error prone if you are doing it manually. Stirling's approximation is (according to Wikipedia) accurate to about 1% for 65!. [strike]That's fine for your application, since you know that 200!/135!65! must be an integer - just use the approximation, do the division, and round off.[/strike]

Edit: Sorry - it's been a long day. 1% of 200! is a big number; my approach will not do if you need an exact answer. However, it'll tell you right off if your calculator can handle the answer. Also, you can use the upper and lower bound formulae to get a sanity check on your answer.

Off to bed now...