Permutations and Combinations (2 Viewers)

[Carrotsticks]

Cannot think of a faster way unfortunately. You could fix the first two shirts (different colour), work out possible cases and then cycle through them (you get the same answer as using Inclusion/Exclusion) but other than that, I've run out of ideas.

Will mull over it but having a hard time doing (and generalising) this particular problem without having to consider some sort of cases.

 

[dunjaaa]

inb4 generalised version in this years BOS Trial, wouldn't be surprised tbh lol

 

[RealiseNothing]

inb4 generalised version in this years BOS Trial, wouldn't be surprised tbh lol

The whole exam is generalised.

You guys better be doing it, I'm doing it again just to see how I go after a year of tutoring it.

 

[seanieg89]

Do you have a similarly easy way of doing Cambridge Year 12 Exercise 10F Q17?

What is the question?

 

[Carrotsticks]

What is the question?

Consider the set of numbers 1,1,2,2,3,3,4,4.

How many permutations are there such that no two identical numbers are immediately adjacent.

 

[seanieg89]

Consider the set of numbers 1,1,2,2,3,3,4,4.

How many permutations are there such that no two identical numbers are immediately adjacent.

Cheers.

It does seem pretty tailor made for inclusion-exclusion, which isn't TOO lengthy. If I can think of something faster later I will post.

 

[braintic]

Cheers.

It does seem pretty tailor made for inclusion-exclusion, which isn't TOO lengthy. If I can think of something faster later I will post.

Note that the answer is 864 which factorises to 2^5 times 3^3.
I was hoping that meant that there was a neat way of getting the answer through multiplication alone.

(The question was actually about shirts, but I guess this is exactly the same)

 

[braintic]

Cheers.

It does seem pretty tailor made for inclusion-exclusion, which isn't TOO lengthy. If I can think of something faster later I will post.

I don't suppose you managed to come up with anything?