A-Level Maths Question

Hello. I'm currently doing some permutations and combinations practice and I encountered this question in my workbook (which does not show the workings in the answers section):

There are 8 violinists. They work in pairs and must sit with their partner. How many seating arrangements are possible.

I got 40320, then checked the mark scheme and it insists the answer is 384. I would like to know how one is supposed to get the correct answer because I really have no idea.

Thank you.

Reply 1

mqb2766

Original post by Sichwünschen

Hello. I'm currently doing some permutations and combinations practice and I encountered this question in my workbook (which does not show the workings in the answers section):
There are 8 violinists. They work in pairs and must sit with their partner. How many seating arrangements are possible.
I got 40320, then checked the mark scheme and it insists the answer is 384. I would like to know how one is supposed to get the correct answer because I really have no idea.
Thank you.

Id agree with 384. How did you come up with yours?

Tbh with questions like these sometimes it useful to do a simplified example where you could write down the answers, so if there were 4 violinists A,B,C.D ad they are paired up as {A,B}, {C.D} can you write down the combinations and work out what your method would give?

(edited 1 month ago)

Reply 2

Sichwünschen

Can you post a full solution please?

Reply 3

mqb2766

Original post by Sichwünschen

Can you post a full solution please?

Theres a sticky at the top of the (maths) forum asking you to post your attempt / saying you shouldnt expect full solutions. So if you post what you tried, happy to give a hint or two.

But its pretty much a one liner if you understand how to do the counting, and that only really comes with practice and thats why I suggested doing the simplified case, if necessary, in the previous post.

Reply 4

sdfj

Original post by Sichwünschen

Can you post a full solution please?

That's not allowed on TSR...

Don't know whether this helps but the method I used (I also got 384) is to find the number of ways to arrange the pairs (ie there are 4 pairs, so how many arrangements of the 4 pairs are possible - that's a very easy calculation) multiplied by the number of arrangements within pairs (ie how many arrangements are possible if the 4 pairs of violinists can switch places within their pairs - again, an easy calculation).

That might look a bit long-winded but it's simply the number of ways to arrange the pairs * the number of arrangements within pairs.

I often notice students (including myself) meddle with choose and permute for these sorts of questions but it's often much easier via other methods.

(edited 1 month ago)

Reply 5

Sichwünschen

Original post by sdfj

That's not allowed on TSR...
Don't know whether this helps but the method I used (I also got 384) is to find the number of ways to arrange the pairs (ie there are 4 pairs, so how many arrangements of the 4 pairs are possible - that's a very easy calculation) multiplied by the number of arrangements within pairs (ie how many arrangements are possible if the 4 pairs of violinists can switch places within their pairs - again, an easy calculation).
That might look a bit long-winded but it's simply the number of ways to arrange the pairs * the number of arrangements within pairs.
I often notice students (including myself) meddle with choose and permute for these sorts of questions but it's often much easier via other methods.

I thought the number of arrangements for all the pairs is 4! (24), and then the number of arrangements within the pair must just be 2?

Or I thought perhaps you had to allocate them all to pairs?

(I'm not very good at this - I just learnt it today)

Reply 6

Harik0

Original post by Sichwünschen

I thought the number of arrangements for all the pairs is 4! (24), and then the number of arrangements within the pair must just be 2?
Or I thought perhaps you had to allocate them all to pairs?
(I'm not very good at this - I just learnt it today)

ok so you have the number of ways to arrange the pairs, and then you have to now factor in how many ways there are to arrange within the pairs. (2 ways for each pair)
(hope this helps but doesnt give too much away)

Reply 7

sdfj

Original post by Sichwünschen

I thought the number of arrangements for all the pairs is 4! (24), and then the number of arrangements within the pair must just be 2?
Or I thought perhaps you had to allocate them all to pairs?
(I'm not very good at this - I just learnt it today)