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27 May 2021, 02:44
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Hello,
If a questions says- 10 people are seated around a circular table. If 2 seating arrangements are said to be different only when positions of people are different relative to each other, in how many ways can these 10 people be seated around that table?
Could any expert please explain the meaning of the above bold statement? I have seen this multiple times in circular permutation question but couldn't quite visualize the same.
Also, can anyone explain the logic behind the permutation formula (n-1)! for such questions?
If a questions says- 10 people are seated around a circular table. If 2 seating arrangements are said to be different only when positions of people are different relative to each other, in how many ways can these 10 people be seated around that table?
Could any expert please explain the meaning of the above bold statement? I have seen this multiple times in circular permutation question but couldn't quite visualize the same.
Also, can anyone explain the logic behind the permutation formula (n-1)! for such questions?
27 May 2021, 19:47
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Hi SDW2,
There's an easy, visual way for you to see exactly what this phrase refers to - and all you will need is a pen and a piece of paper:
1) Draw a circle.
2) Write the numbers 1 - 10 around the edge off the circle. These numbers represent the 10 chairs.
3) Rotate the paper.
Notice how any of the ten numbers can be at the 'top' of the circle, but the relative positions of the 10 numbers is always the SAME (for example, #2 is always between #1 and #3). These are NOT 10 different arrangements; it's 1 arrangement (because the table is a circle). This is why you have to adjust your calculation when dealing with these types of questions.
GMAT assassins aren't born, they're made,
Rich
There's an easy, visual way for you to see exactly what this phrase refers to - and all you will need is a pen and a piece of paper:
1) Draw a circle.
2) Write the numbers 1 - 10 around the edge off the circle. These numbers represent the 10 chairs.
3) Rotate the paper.
Notice how any of the ten numbers can be at the 'top' of the circle, but the relative positions of the 10 numbers is always the SAME (for example, #2 is always between #1 and #3). These are NOT 10 different arrangements; it's 1 arrangement (because the table is a circle). This is why you have to adjust your calculation when dealing with these types of questions.
GMAT assassins aren't born, they're made,
Rich
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