inclusion exclusion

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kory

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I'm working on some inclusion/exclusion problems and I'm not sure what to do here. I followed some other examples but I'm not getting the correct answer.



Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions.

If the N's are placed first, how many ways are there to choose positions for them?

My solution:
n = 8 by combing the Ns into one and subtracting that from the total 9 letters
n1 = 1 because there is one N (combined)
n2 = 2 because there are two S
n3 = 4 because there is four E
n4 = 1 because there is one T

8! /( 1! * 2! * 4! * 1! ) = 40320 / 48 = 840.......Those parentheses are important


840 isnt the answer. Not sure what I'm doing wrong here...any suggestions?
 
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kory said:
Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions.

If the N's are placed first, how many ways are there to choose positions for them?
Click to expand...
Can you show us Example 9.5.11 so we can be sure what technique is expected?

Also, what you have done answers a different question than they have asked (in the part you quoted).
 
Thanks. It looks like your reference to "inclusion exclusion" was misleading! In addition, you haven't followed the example at all.

So, how many ways are there to place the two N's in your problem? That will correspond to just the first factor in their work.

And does the problem continue after the one question you showed us, and actually find the total count as in the example? The answer to that will not be what you showed, either.
 
The images are from the 9.5.11 example that the original question is referring to. Its an example that shows the number of the combinations of the word "mississippi". The total count was 34,650.
But the problem i'm on isnt asking for all of the combinations for the word "tennessee"....its asking for all of the combinations of "tennessee" if the "nn" were positioned first. Therefore the example that they want me to refer to for help isnt helping. Its a completely different scenario.
 
kory said:
The images are from the 9.5.11 example that the original question is referring to. Its an example that shows the number of the combinations of the word "mississippi". The total count was 34,650.
But the problem i'm on isnt asking for all of the combinations for the word "tennessee"....its asking for all of the combinations of "tennessee" if the "nn" were positioned first. Therefore the example that they want me to refer to for help isnt helping. Its a completely different scenario.
Click to expand...
I think you're misunderstanding the problem. They are explicitly telling you to do what they did in the example, so it must be applicable!

Moreover, it's meaningless to talk about 'all of the combinations of "tennessee" if the "nn" were positioned first.' (I'll ignore the fact that you don't really mean "combinations" at all, but "orderings", which are in effect "permutations".) How you make an ordering is unrelated to what it is. Show me one of your orderings; can you tell whether I placed the Ns or the Es first?

Here is the problem as you quoted it:
kory said:
Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions.

If the N's are placed first, how many ways are there to choose positions for them?
Click to expand...
Clearly there are more questions following this; what are they? I'm guessing that they are something like "Then, how many ways are there to place the E's?" If not, we need to know.

But as I read it, this parallels the start of the example:

1619641255724.png​

In your problem, there are 9 positions in all; so there are [MATH]{9\choose 2}[/MATH] ways to place the N's. I think that's what they're asking for.

But, again, I can't know until I know what you know about the entire problem. (This is why our guidelines ask you to show all of it: "Post the complete text of the exercise. This would include the full statement of the exercise including the instructions".)
 
If the E's are placed second, how many ways are there to choose positions for them?

If the S's are placed third, how many ways are there to choose positions for them?

If the T is placed fourth, how many ways are there to choose a position for it?
 
kory said:
If the E's are placed second, how many ways are there to choose positions for them?

If the S's are placed third, how many ways are there to choose positions for them?

If the T is placed fourth, how many ways are there to choose a position for it?
Click to expand...
That's just what I expected. So they are leading you through the process of the example, step by step, even taking E next as I suggested.
 
kory said:
I'm working on some inclusion/exclusion problems and I'm not sure what to do here. I followed some other examples but I'm not getting the correct answer.
Click to expand...
\(TE\boxed{NN}ESSEE \) The number of ways the rearrange that string of eight symbols is:
\(\dfrac{8!}{4!\cdot 2!}=840\) SEE HERE

Don't over-think these! he number of ways the rearrange the string, \(***||||00000\) is:
\(\dfrac{12!}{5!\cdot 4!\cdot 3!}\)
 
pka said:
\(TE\boxed{NN}ESSEE \) The number of ways the rearrange that string of eight symbols is:
\(\dfrac{8!}{4!\cdot 2!}=840\) SEE HERE

Don't over-think these! he number of ways the rearrange the string, \(***||||00000\) is:
\(\dfrac{12!}{5!\cdot 4!\cdot 3!}\)
Click to expand...

I dont understand where you got 12! from
 
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