ahh the permutations...

[arginine1]

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Alright.. I thought I had this topic down cold but I guess I don't?


On one of the tests from top score there is a question:

"How many arrangements can 6 people be seated round a circular table?"

a. 21
b. 24
c. 120
d. 720
e. 810

I thought you can assign numbers to each position (as in 6 different people possible in the 1st seat * 5 people in the second seat * 4 in the third... and so on.. until you cover all seats). So my answer comes out to 720 (6*5*4*3*2*1), theirs to 120.

Can anyone elaborate on this? Explain?

 

[baedero1]

Alright.. I thought I had this topic down cold but I guess I don't?


On one of the tests from top score there is a question:

"How many arrangements can 6 people be seated round a circular table?"

a. 21
b. 24
c. 120
d. 720
e. 810

I thought you can assign numbers to each position (as in 6 different people possible in the 1st seat * 5 people in the second seat * 4 in the third... and so on.. until you cover all seats). So my answer comes out to 720 (6*5*4*3*2*1), theirs to 120.

Can anyone elaborate on this? Explain?

(n-1)! = 5! = 5*4*3*2*1 = 120

 

[NumbaOneStunna]

Alright.. I thought I had this topic down cold but I guess I don't?


On one of the tests from top score there is a question:

"How many arrangements can 6 people be seated round a circular table?"

a. 21
b. 24
c. 120
d. 720
e. 810

I thought you can assign numbers to each position (as in 6 different people possible in the 1st seat * 5 people in the second seat * 4 in the third... and so on.. until you cover all seats). So my answer comes out to 720 (6*5*4*3*2*1), theirs to 120.

Can anyone elaborate on this? Explain?

You're right if we had six different seats arranged in a line with six different people we'd have 720 ways to arrange them. The tricky thing about this one is that it's not really asking how many ways can we arrange them with different chairs, it's asking about the number of ways we can position people relative to each other.

So for every possible ordering of people for example A B C D E F (where the letters are people) you can take that order keep it the same and have everyone move to the right a seat an still have the same order. This gives us six times as many arrangements when we look at what chair they're in, but if we look at the order of people we only get less arrangments. Hence the answer should be 6! / 6 = 120. I also missed this one, making the same mistake =p - this problem is a bit ambiguous though because both interpretations are valid imo.

 

[arginine1]

You're right if we had six different seats arranged in a line with six different people we'd have 720 ways to arrange them. The tricky thing about this one is that it's not really asking how many ways can we arrange them with different chairs, it's asking about the number of ways we can position people relative to each other.

So for every possible ordering of people for example A B C D E F (where the letters are people) you can take that order keep it the same and have everyone move to the right a seat an still have the same order. This gives us six times as many arrangements when we look at what chair they're in, but if we look at the order of people we only get less arrangments. Hence the answer should be 6! / 6 = 120. I also missed this one, making the same mistake =p - this problem is a bit ambiguous though because both interpretations are valid imo.

That makes sense now.. your explanation that is, not the problem.. I hate when they word it in a way where multiple interpretations are possible. As if this test isn't hard enough😡

Thanks for your help 🙂