How can I get spotlight to recognise expressions like
I want to do combinations and permutations with spotlight.
After proper transformations you can calculate at least simple combinations and permutations in Spotlight:
7P4=7!/(7-4)!=7!/3!. Entered in Spotlight as
7!/3! it will give you a proper result: 840.
C(8,5)=8!/5!(8-5)!=8!/5!3!. Entered in Spotlight as
8!/5!3! it will give you a proper result: 56.
For info on other advanced functions besides Factorial which Spotlight can handle, see this page
According to Google Search a WolframAlpha Spotlight plug-in for Flashlight (a Spotlight extender - link in the other answer) which should be capable of doing these kind of calculations once existed but I can't actually find it or it's gone.
With Google Chrome installed you can use a work-around and add the Wolfram | Alpha extension which supports expressions like in your question in the extra search bar:
There is no easy way to do this.
Spotlight has access to doing calculations with the built-in Calculator.app, so you can put in some simple arithmetic expressions. However, this app is not able to compute combinations/permutations.
There seems to be something you can install called Flashlight (http://flashlight.nateparrott.com) that will let you write custom plugins for Spotlight, so maybe that is a solution (I have never used it, so I don't know how easy or difficult it would be).