Perms and combs question (1 Viewer)

[deswa1]

Hey guys,

Can someone help me with this question (from Cambridge)? I might add some more questions later if I find more I can't do:

- Bob is about to hang his 8 shirts in the wardrobe. He has 4 different styles of shirt, two identical ones of each particular style. How many different arrangements are possible if no two identical shirts are next to one another?

Thanks a lot

 

[Demento1]

Seen this question before. Quite tedious. Do you want some hints or straight off the bat working out?

 

[Fawun]

Seen this question before. Quite tedious. Do you want some hints or straight off the bat working out?

You're in year 10?

 

[deswa1]

Seen this question before. Quite tedious. Do you want some hints or straight off the bat working out?

Yeah a decent hint would be enough I think. I tried something but got a bit off the answer so yeah, if you could point in the right direction or summarise the working (like just roughly what you're are doing rather than actually doing it) it should be great thanks

You're in year 10?

He's a genius (srs)

 

[RealiseNothing]

There was a thread for this exact question before, I'll try find it.

 

[Demento1]

Yeah a decent hint would be enough I think. I tried something but got a bit off the answer so yeah, if you could point in the right direction or summarise the working (like just roughly what you're are doing rather than actually doing it) it should be great thanks



He's a genius (srs)

Alright. Think like this: Have you worked out the total number of permutations for 8 shirts, whilst taking into account identical pairs?

 

[Carrotsticks]

I'll give you somewhere to start:

Let the shirts be A,A,B,B,C,C,D,D.

Now we fix 4 distinct shirts.

||||A||||B||||C||||D||||

We have 4 distinct shirts left, and the |||| indicates a gap where a shirt can be inserted.

First shirt A can have 3 spots to go inside, since it cannot go into the position next to the A. So for example we have something like:

||||A||||B||||C||||D||||A||||

Second shirt B has 4 shirts to go inside. By adding another shirt, we have added another space for a shirt to go inside etc etc.

Will finish it off later if you don't because I'm at Fisher Library atm and the lights are slowly turning off 1 by 1, and it's nearly pitch black now on this floor.

I am going to get murdered in the dark and my last act was helping you with this question.

 

[RealiseNothing]

http://community.boredofstudies.org/showthread.php?t=286956

Not sure if this helps.

 

[RivalryofTroll]

I was thinking:

no. of different arrangements where no two identical shirts are next to one another = total different arrangements - no. of different arrangements where two identical shirts ARE next to one another

but dats wrong probs.