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 #3
avatar+2511 
+5

For each of the partitioned sets, calculate the unique permutations using N!/((d1!)* (d2!) *...(dz!)) Where N is the number of elements and dz is the number of repeated elements (d) of each kind (Z).  Ex:  for 4,2,2,1,1  it’s 5!/((2!)*(2!)) = 30. This represents 30 uniquely identifiable arrangements.  

 

\(\begin{array}{|r|r|r|r|r|r|r|r|r|} \hline \overset {..}\smile &G & I & N & G & E & R&A &L &E & \overset {..}\smile \\ \hline 10 & & & & & & & & & & 1\\ \hline 9 & 1 & & & & & & & & & 2 \\ \hline 8 & 2 & & & & & & & & & 2 \\ \hline 8 & 1 & 1 & & & & & & & & 3 \\ \hline 7 & 3 & & & & & & & & & 2 \\ \hline 7 & 2 & 1 & & & & & & & & 6 \\ \hline 7 & 1 & 1 & 1 & & & & & & & 4 \\ \hline 6 & 4 & & & & & & & & & 2 \\ \hline 6 & 3 & 1 & & & & & & & & 6 \\ \hline 6 & 2 & 2 & & & & & & & & 3 \\ \hline 6 & 2 & 1 & 1 & & & & & & & 12 \\ \hline 6 & 1 & 1 & 1 & 1 & & & & & & 5 \\ \hline 5 & 5 & & & & & & & & & 1 \\ \hline 5 & 4 & 1 & & & & & & & & 6 \\ \hline 5 & 3 & 2 & & & & & & & & 6 \\ \hline 5 & 3 & 1 & 1 & & & & & & & 12 \\ \hline 5 & 2 & 2 & 1 & & & & & & & 12 \\ \hline 5 & 2 & 1 & 1 & 1 & & & & & & 20 \\ \hline 5 & 1 & 1 & 1 & 1 & 1 & & & & & 6 \\ \hline 4 & 4 & 2 & & & & & & & & 3 \\ \hline 4 & 4 & 1 & 1 & & & & & & & 6 \\ \hline 4 & 3 & 3 & & & & & & & & 3 \\ \hline 4 & 3 & 2 & 1 & & & & & & & 24 \\ \hline 4 & 3 & 1 & 1 & 1 & & & & & & 20 \\ \hline 4 & 2 & 2 & 2 & & & & & & & 4 \\ \hline 4 & 2 & 2 & 1 & 1 & & & & & & 30 \\ \hline 4 & 2 & 1 & 1 & 1 & 1 & & & & & 30 \\ \hline 4 & 1 & 1 & 1 & 1 & 1 & 1 & & & & 7 \\ \hline 3 & 3 & 3 & 1 & & & & & & & 4 \\ \hline 3 & 3 & 2 & 2 & & & & & & & 6 \\ \hline 3 & 3 & 2 & 1 & 1 & & & & & & 30 \\ \hline 3 & 3 & 1 & 1 & 1 & 1 & & & & &15 \\ \hline 3 & 2 & 2 & 2 & 1 & & & & & & 20 \\ \hline 3 & 2 & 2 & 1 & 1 & 1 & & & & & 60 \\ \hline 3 & 2 & 1 & 1 & 1 & 1 & 1 & & & & 42 \\ \hline 3 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & & 8 \\ \hline 2 & 2 & 2 & 2 & 2 & & & & & & 1 \\ \hline 2 & 2 & 2 & 2 & 1 & 1 & & & & & 15 \\ \hline 2 & 2 & 2 & 1 & 1 & 1 & 1 & & & & 35 \\ \hline 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & & & 28 \\ \hline 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & 9 \\ \hline 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \overset {..}\smile &G & I & N & G & E & R&A &L &E & \downarrow \\ \hline \end{array}\\ \small \text {Sum of all unique permutations } \hspace{2.85cm} \fbox {512}\\\)

 

EDIT: Corrected Errors

GA

21.06.2018
 #11
avatar+2511 
+4

This is hilarious!

The reason I thought you were Mr. BB, is your presentation of this formula/equation

[3 + 3 - 1] nCr 3 =5C3 = 5! / [5 - 3]!. 3! = 10

in irregular mathematical syntax. I usually refer to this style as SLOP, because that is what it is. (It looks like the factorial of 3 = 10)

 

Mr. BB presents his formula/equations in a very similar sloppy format –though he often uses curly braces. Here’s an example: https://web2.0calc.com/questions/please-help_33396#r1

 

Mr. BB is a master at presenting slop, well beyond irregular mathematical syntax; he also has an incredibly high error rate—not just typos, it’s a bounty of misinformation presented with authority and irritation. This post elaborates and describes Mr. BB.

https://web2.0calc.com/questions/a-bag-contains-different-colored-beads#r10

Excerpt:

...Mr. BB, the stubborn, relentless, intractable Blarney Banker of lore: a pseudo intellectual with a multiplicity of advanced dimwit degrees in arrogant stupìdity, a professor of misinformation, who teaches with authority and irritation.

 

Here’s a post he made to improve on one of your answers:

https://web2.0calc.com/questions/working-with-formulas-help

 

Here, demonstrating his finesse with Latin:

https://web2.0calc.com/questions/please-help-solve_7

 

Here, demonstrating his finesse with coding. There’s also history about Mr. BB’s first troll, 14-YO Dragonlance. Along with other names, he called him the “Banker Man.” I call him the “Blarney Banker,” aka Mr. BB

https://web2.0calc.com/questions/a-question-of-rationality

 

Here’s an anonymous troll commenting on Mr. BB: 

https://web2.0calc.com/questions/help-difficult#r5

I went blind laughing at this. I did again after rereading it for this post.

It’s so damn true!

 

There are many more if you care to peruse my profile –some are quite funny!

 

Anyway, EP, I probably wouldn’t have trolled you if your name were attached –at least not in this manner.

--

Curious question: do you ever use “G’day” as a valediction without the sarcastic overtones?

 

 

GA  

20.06.2018
 #9
avatar+2511 
+2

You shouldn’t delete your posts, Mr. BB.

 

According to experts, there should be:

[3 + 3 - 1] nCr 3 =5C3 = 5! / [5 - 3]!. 3! = 10 ways of putting the lamps on the tables.

 

You should just not make them in the first place!

 

You should also update your “expert” consultants list.  If you put my name at the top of the list,  then you will always have the correct answers.

 

GETSMART should really be at the top of your list though. He is your Christmas present and his genetic enhancement includes optimization to teach you. You are not a very good student, so he prefers to spend most of his time pecking bugs from your surroundings, while waiting for Thanksgiving.   

 

 

GA

20.06.2018