A chap in the company I worked for had the job of calculating spares holding for equipments we'd sold and were supporting. He came to me with some very expensive software which was supposed to help him do this. It worked fine for small numbers - up to a few hundreds or thousands - but in the quantities he was dealing with, it gave the ridiculous result that the more equipments you were supporting, the fewer spares you needed to hold!
I investigated and found they'd attempted to calculate the factorials explicitly and than divide them. These numbers are huge and quickly overflowed the machine's arithmetic. In fact, the trick is to multiply and divide alternately so keeping the numbers a lot smaller. It proved easy to modify the code. Problem solved.
So I wrote to the company who'd supplied the software pointing out that it misbehaved and offered to tell them how to put it right and was promptly offered a grand to do so. I sent them little more than what is in this post and the code patch we'd made, they paid up like gents. I put my share towards a new piano!
You can also use Stirlings approximation for factorials, although it's not much help in simple sums like this in my experience. If you are doing a more complex analytic analysis, you can often do a bit of cunning cancelling and get a nice proof using it.
You may find this interesting if you are interested in very big factorials and the like:
Wallasey is rampant with crime Soon as i retire soom im leavin The police are useless & dont turn up to most jobs At night its like 90s LA with the rozzer copter over wallasey Wakes me up too often Its a weird reality that a smack head on the dole with drugs paid for by taxpayers can go into tesco, rob £60 worth of steaks , no one will stop him, police wont turn up & and the cost is paid by shoppers ( workers ,taxpayers) Its a circle of apathy , weakness & self entitlement of even the bag heads. The taxpayers funds EVERYTHING in the uk even crime
Serious sexual assault reported last week (not Wallasey) and the assaulted person still waiting to be seen by the police. Are they that overworked or that few of them. Frinds a traffic cop down south, retires in 4 years on a pension more than I am earning...think it might be me nicking the £60 super market meat in a few years..Get Dilly to engineer a secret compartment on a zimmer frame to stash it in.
I know a co op area manager...they lose 14 million nationally of meat per year. No staff is goin to stop ... bags esp druggys for £7 an hr. Ah well good ol people who buy food will pay....yawn
The news this morning informs us that child arrest figures have been drastically reduced, I have always wondered how they define a child, to what age does someone remain a child? is this why we have the rise in street crime because the police don't attend alleged child / youth crime? has this has given rise to gangs of feral youths roaming around Wirral until the early hours house breaking, stealing cars and motorcycles, thieving from cars and creating vandalism and mayhem where ever they go,it appears with a certain amount of immunity all under the guise of anti social behaviour, perhaps if they were honest they should call it what it is, criminality.
