What is the equivalent of winning the lottery in the software tester’s context? How do you as a tester win your own special little lottery? In order to answer these questions let’s have a look on what the chances are that you win the “real” lottery. We can do that backwards, starting with the solution:

The chances for you to win the lottery (select 6 out of 45 numbers) is exactly 1 : 8’145’060

But, how do we know?

Ok, we have 45 different numbers or slots:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
For those of you who have not skipped my last post know that for each of the slots we have the following amount of declining possibilities to select numbers:
45 x 44 x 43 x 42 x 41 x 40 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
And because we only have to choose 6, we stop at 40.

This can also be expressed as:
Like: 45 x 44 x 43 x ….. x 3 x 2 x 1 divided by anything in the row below 40 as they are not needed. That is the elegance of math. Isn’t it beautiful?

I know, you have already quickly calculated the result in your head and you must have arrived with the number 5’864’443’200, which, obviously, is not equal to 8’145’060. And you are right. And I am right, too. I have not said I am finished yet. Sneaky me!

We now have the calculation of: “In how many ways can a set of 6 be chosen out of a stack of 45 including different orders of the six cards”. But the lottery does not care if one of the winning numbers is selected as a first number or as a last. Neither does the winner care in his bliss of the millions whether or not he crossed one or the other number first on his tiny receipt.

In how many ways can a set of 6 be grouped? You remember the evil mobbing bunch of memorial picture taking testers from the last post? No? Ok, here is the explanation once more: Six factorial, or 6 x 5 x 4 x 3 x 2 x 1 = 720

That is the number we have to divide the whole thing by, before we hop off to cash the winner’s cheque with the grumpy old lady behind the cashier’s desk.

Or written as a formula:

Or even more elegantly:

Or even more generally -> BTW: If you want to actually say that to - let’s say: to a person who has very dark sun glasses and therefore cannot see the formula - then say: “n choose k” and everybody will immediately believe you are a highly professional software tester.

So = 8’145’060

Which stated as a probability is:

QED

This leads us to the intriguing question: Why on earth am I dwelling on math formulas? That is because after having recommended Khan Academy in the last post, I ate my own dog food. And now I am hooked. I joyfully participate in Khan Academy’s exercises. And man, I wanna get one of those Black Hole Badges. Any would be ok, but “Tesla” is the one I fancy.



I need to add a 3rd part to this series in order to close the loop back to actionable value for software testing. Next time will be about pair-wise testing and why it is not “Best Practise”. Sometimes it is not even “Good Practise”. It may indeed be “Totally Crappy Practise” in some context.

Ah, almost forgot: In the next post I’ll also tell you how to win your own special little lottery (Justin: I’ll address your requests, too). So, stay tuned!

tags: mathematics, permutations, pair wise testing