Permutations/Combinations (1 Viewer)

[michaeljennings]

A tea party is arranged for 16 people along two sides of a table with 8 seats on each side. Four people wish to sit on one particular side and two on the other side. How many ways can they be seated

The answer is 8P4 times by 8P2 times by 10!

Could someone please explain this to me. I have a very hard time understanding this topic and i am sure to fail my trial exam

 

[Some Vunt]

A tea party is arranged for 16 people along two sides of a table with 8 seats on each side. Four people wish to sit on one particular side and two on the other side. How many ways can they be seated

The answer is 8P4 times by 8P2 times by 10!

Could someone please explain this to me. I have a very hard time understanding this topic and i am sure to fail my trial exam

16 - 4 for the first group on one side and then - 2 for the group on the other side then factorial. And the 8P2 and 8P4 are the groups on either side.

 

[michaeljennings]

the 8P2 and 8P4 are the groups on either side.

Could you explain this part too me i dont understand it why isnt it 8C4 times by 8C2

 

[tambam]

Could you explain this part too me i dont understand it why isnt it 8C4 times by 8C2

It can't be a combination because it specifies an arrangement of where they sit, and not just a group, therfore its a permutation

So,
There are 2 sides of the table, with 8 seats on each side.
4 people must sit on one side. They have 8 seats to choose from, so from 8, selecting 4, where order is important = 8P4
In the same way, the other side is 8P2.
There are then 10 seats left, and 10 people left to be seated. So, 10P10= 10!

And then you times them all together, to get 8P4x8P4x10! for all possible combinations

 

[michaeljennings]

They have 8 seats to choose from, so from 8, selecting 4, where order is important = 8P4

I still dont understand?? Where does it say that order is important

 

[Hermes1]

I still dont understand?? Where does it say that order is important

in the definition of combinations and permutations

permutation - ordered selection
combination - unordered selection

 

[tambam]

I still dont understand?? Where does it say that order is important

Its a seating ARRANGEMENT, so there is a specific spot for each person, which is another way of saying the order is important.

A combination (C) is only used when you just need to pick a group, and not place the people in specific positions. Eg. If you had 4 spots in a committee and had 8 people to choose from, it would be 8C4.

Seating arrangements are always permutations.

 

[michaeljennings]

in the definition of combinations and permutations

permutation - ordered selection
combination - unordered selection

But the 4 people can sit anywhere out of the 8 seats cant they?

 

[michaeljennings]

Its a seating ARRANGEMENT, so there is a specific spot for each person, which is another way of saying the order is important.

A combination (C) is only used when you just need to pick a group, and not place the people in specific positions. Eg. If you had 4 spots in a committee and had 8 people to choose from, it would be 8C4.

Seating arrangements are always permutations.

Ohhh i see

 

[Hermes1]

Its a seating ARRANGEMENT, so there is a specific spot for each person, which is another way of saying the order is important.

A combination (C) is only used when you just need to pick a group, and not place the people in specific positions. Eg. If you had 4 spots in a committee and had 8 people to choose from, it would be 8C4.

Seating arrangements are always permutations.

lol. tnk god this topic is not in my trial.

 

[tambam]

lol. tnk god this topic is not in my trial.

Haha, this isn't even a particularly hard question.
You should see the ones that are actually ridiculously hard and complicated and impossible to do.

 

[Hermes1]

Haha, this isn't even a particularly hard question.
You should see the ones that are actually ridiculously hard and complicated and impossible to do.

lol. cant wait.

 

[XTsquared]

You can answer this question using combinations however:

Of 16 people, 4 on on side and 2 on the other (hence 10 others)
Therefore we must choose six to sit with the two on one side = 10C6
We must choose the remaining four to sit with the other four on the other side = 4C4
We can arrange one side in 8! ways, the other side in 8! ways.

Hence in total: (8!)(8!)(10C6)(4C4) ways (which comes out as the same answer as (8P4)(8P2)(10!) ).

What people seem to not understand is you can pick a group then arrange it, you don't have to arrange from the get go.

 

[failwhale]

fuk perms and combs 4 lyf

 

[Hermes1]

fuk perms and combs 4 lyf

lol. is it really that bad. this is the only topic we havent started at skool.

 

[michaeljennings]

lol. is it really that bad. this is the only topic we havent started at skool.

Hardest topic in ext 1 by far

 

[Omnipotence]

lol. is it really that bad. this is the only topic we havent started at skool.

I hate 4U Perms and Combs.
Edit: I despise Probability aswell.

 

[michaeljennings]

I hate 4U Perms and Combs.
Edit: I despise Probability aswell.

+1, if i see it in an exam i just assume they are marks that will be lost

 

[tambam]

lol. is it really that bad. this is the only topic we havent started at skool.

It can be really simple and straight forward, or its just wtf makes no sense. Soe scenarios are really hard to gett your headd around

I think at our school they decided to start teachiing us in year11 just so we could have more time to make sense of it

 

[Omnipotence]

Yeah, I was taught Perms and Combs near the start of Yr 11.