Discrete Math - 6.1.1 Counting Rules

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[@seydinamouhamedgueye4266]

Hi, I have a question regarding the example on division rule.
In this case, are you just considering the fact that the arrangement can happen only clockwise and not anticlockwise ? Why did you not multiply the divisor by 2 to handle both cases ? Thank you

[@Legac3e]

Rotating anticlockwise once is the same as rotating clockwise 5 times. So, hers accounted for A starting one to the left already on the 5th rotation without considering any anticlockwise moves.
I hope that helps. :)

[@weaponkid1121]

ok I'm following up to the point where you use the 6 to divide... You found 6 orders that are technically the same arrangement, sure, makes sense, but why do you then divide by 6? Shouldn't you subtract by 6? Obviously you divide because it's an example for the division rule, but I don't understand why you divide other than that

[@hunyoungha2550]

Because there are other combs that are considered the same. As she says ABCDEF is the same as BCDEFA, CDEFAB, etc. And if you have arrangements like ACEBDF, then CEBDFA and EBDFAC, etc, would be considered the same with ACEBDF. And there are a whole bunch of them. ( in this case, 600) and therefore instead of finding the actual number of other combs to subtracting it, divide it by 6 would be a more time-saving method.

[@nurhayatiaiman9104]

@@hunyoungha2550 Thank you! You actually made me understand the point of this theorem

[@brettrietveld621]

You divide by 6 because for each position you find from 6! there are 6 equivalent ones, so divide the total by 6

[@danixdanny3059]

For any new people who might see this, I best understood it this way:
For the sequence ABCDEF, there are a total of six ways I can arrange these letters that would be considered identical because they can be achieved by simply rotating the letters around the table. So:
ABCDEF / BCDEFA /CDEFAB / DEFABC / EFABCD / FABCDE. A total of six arrangements are considered to be the same ONE arrangement.
This is why we are dividing by 6.

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