Permutations & Probability - A Revisit to your Math Class - Part I
08.01.12 - 12:43 - Filed in: Software Testing
What’s the relationship between Testers and Mathematics? I don’t know. But I know what it should be. It should be one of affectionate care and love. Let’s have a short experiment: Upon hearing the following two words: Permutations & Probability. Don’t you immediately start to smile? I do.
The subject of permutations came up when I recently had a coaching session with James Bach and we had some discussions on pair wise testing and the selection of test cases.
For today let’s start simple:
If you are a team of five fabulous testers and you are keen to have a picture taken as a memory of the equally fabulous project you just finished. In how many different orders can you place yourselves smiling towards the camera?
The blunt answer without explanation is: 5!
The ones among you who have never liked mathematics may ask: “Why do you shout? Why do you put an exclamation mark after the answer that is not such a huge number after all?”
And I reply: That’s because it is bigger than you think and because the answer is not “a shouted 5”, but 5 factorial, which is 5 x 4 x 3 x 2 x 1 = 120 possible configurations of a picture of a fabulous team of 5 testers.
Why is that so? Well for the picture of 5 testers you have five slots: _ _ _ _ _ . And you have all 5 testers eagerly waiting to get on one of the slots. One of the five takes the first slot (so there are 5 possibilities for the first slot): 5 _ _ _ _ . Then the remaining 4 testers viciously fight for the second slot: 5 x 4 _ _ _. And so on until we have: 5 x 4 x 3 x 2 x 1
That leads us to a meaner example: Let us therefore assume you were not 5 testers on the project but 6. And now it comes: One of the six testers did not contribute to the success of the fabulousness at all. Obviously, you would not want to have that 6th tester on your memory picture. You now have 6 testers of which only 5 will eventually be on the picture: But, how many possibilities?
The answer is: 720
No shouting, no exclamation marks, but an amazing amount of possible constellations for bullying one of the 6 testers out of a memorial picture. The calculation goes as follows: 6 x 5 x 4 x 3 x 2.
That’s all for today. Next time there will be some hairy examples of ordered and not ordered sets and the calculation of the probability of winning the lottery.
Do I hear your voices demanding: “Come on, give us at least one more useful link!”?
Ok, here you go: Khan Academy
The subject of permutations came up when I recently had a coaching session with James Bach and we had some discussions on pair wise testing and the selection of test cases.
For today let’s start simple:
If you are a team of five fabulous testers and you are keen to have a picture taken as a memory of the equally fabulous project you just finished. In how many different orders can you place yourselves smiling towards the camera?
The blunt answer without explanation is: 5!
The ones among you who have never liked mathematics may ask: “Why do you shout? Why do you put an exclamation mark after the answer that is not such a huge number after all?”
And I reply: That’s because it is bigger than you think and because the answer is not “a shouted 5”, but 5 factorial, which is 5 x 4 x 3 x 2 x 1 = 120 possible configurations of a picture of a fabulous team of 5 testers.
Why is that so? Well for the picture of 5 testers you have five slots: _ _ _ _ _ . And you have all 5 testers eagerly waiting to get on one of the slots. One of the five takes the first slot (so there are 5 possibilities for the first slot): 5 _ _ _ _ . Then the remaining 4 testers viciously fight for the second slot: 5 x 4 _ _ _. And so on until we have: 5 x 4 x 3 x 2 x 1
That leads us to a meaner example: Let us therefore assume you were not 5 testers on the project but 6. And now it comes: One of the six testers did not contribute to the success of the fabulousness at all. Obviously, you would not want to have that 6th tester on your memory picture. You now have 6 testers of which only 5 will eventually be on the picture: But, how many possibilities?
The answer is: 720
No shouting, no exclamation marks, but an amazing amount of possible constellations for bullying one of the 6 testers out of a memorial picture. The calculation goes as follows: 6 x 5 x 4 x 3 x 2.
That’s all for today. Next time there will be some hairy examples of ordered and not ordered sets and the calculation of the probability of winning the lottery.
Do I hear your voices demanding: “Come on, give us at least one more useful link!”?
Ok, here you go: Khan Academy
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