how to calculate 1 - (nCr(1209, 100) / nCr(1300, 100)) ?

You can simplify it as follows (where the capital pi symbol means take the product of what follows).  However, the site calculator doesn't have this product function as far as I can tell.

1-(nCr(1209,100)/nCr(1300,100))=

Okay, yes the numbers are too large.  I do not think that you will get it to work on this calculator.

Have a look here.

http://www.wolframalpha.com/input/?i=1-%28nCr%281209%2C100%29%2FnCr%281300%2C100%29%29%3D&dataset=