bigmansouf
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Question:
in how many ways can the letters of the word NOTATION be arranged?hr

the answer from the book states 5040 which is 7!
i thought that the answer is 8!

Please can someone explain why the answer is 5040.
i thought since NOTATION has 8 words, the answer is 8!

thanks for helping
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mqb2766
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N, O and T are repeated. How does that affect things?
(Original post by bigmansouf)
Question:
in how many ways can the letters of the word NOTATION be arranged?hr

the answer from the book states 5040 which is 7!
i thought that the answer is 8!

Please can someone explain why the answer is 5040.
i thought since NOTATION has 8 words, the answer is 8!

thanks for helping
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the bear
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(Original post by bigmansouf)
Question:
in how many ways can the letters of the word NOTATION be arranged?hr

the answer from the book states 5040 which is 7!
i thought that the answer is 8!

Please can someone explain why the answer is 5040.
i thought since NOTATION has 8 words, the answer is 8!

thanks for helping
if a letter is repeated 3 times you divide by 3! to remove the duplicates.
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bigmansouf
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so it would be  \frac{8!}{3!} but this is 1120
(Original post by the bear)
if a letter is repeated 3 times you divide by 3! to remove the duplicates.
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mqb2766
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If only N was repeated, how many would you divide by?
If N and O were repeated, how many would you divide by?
If ....
(Original post by bigmansouf)
so it would be  \frac{8!}{3!} but this is 1120
No, bear's example was for a single letter which occurs three times.
You have three letters, each occurring twice.
Last edited by mqb2766; 5 months ago
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the bear
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(Original post by bigmansouf)
so it would be  \frac{8!}{3!} but this is 1120
i could not give too much information away because of the rules. mqb has given some useful hints.
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bigmansouf
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(Original post by the bear)
i could not give too much information away because of the rules. mqb has given some useful hints.
(Original post by mqb2766)
If only N was repeated, how many would you divide by?
If N and O were repeated, how many would you divide by?
If ....

No, bear's example was for a single letter repeated occurring times.
You have three letters, each occurring twice.
I used the hints you and the bear gave me


So the word is N O T A T I O N

letters : a, i, o, o, t, t, n, n ( 8 letters in total but 3 are repeated) (when the repeated are not counted there is 5)

_ _ _ _ _ _ _ _
for the first place there are 5 letters to choose from. Lets choose N. (there are 5 ways)
N

letters : a, i, o, o, t, t, n, ( 7 letters in total but 2 are repeated) (when the repeated are not counted there is 5)


_ _ _ _ _ _ _

Lets choose N. (there are 7 ways to choose the second place)
NN

letters : a, i, o, o, t, t, ,( 6 letters in total but 2 are repeated) (when the repeated are not counted there is 4)


_ _ _ _ _ _

Lets choose A. (there are 4 ways to choose a letter for the 3rd place)
NNA

letters : i, o, o, t, t, ( 5 letters in total but 2 are repeated) (when the repeated are not counted there is 3)

Basically i continue to do this until i fill up all the places. There are 5 x 7 x 4 x 3 x 2 x 3 x 2 x 1 = 5040 ways


_ _ _ _ _

Lets choose I. (there are 3 ways to choose the 4th place)
NNAI

letters : i, o, o, t, t, ( 5 letters in total but 2 are repeated) (when the repeated are not counted there is 3)


_ _ _ _ _

for the 5th place there are 7 letters to choose from. Lets choose I. (there are 3 ways to choose the 4th place)
NNAIT
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mqb2766
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A hard way to proceed because of the branching which occurs. Just go with your original 8! idea/arrangement.

If one letter is repeated (occurs twice) what would you divide the total number by?
If two letters are repeated (both occur twice) what would you divide by
... for three letters ...

(Original post by bigmansouf)
I used the hints you and the bear gave me


So the word is N O T A T I O N

letters : a, i, o, o, t, t, n, n ( 8 letters in total but 3 are repeated) (when the repeated are not counted there is 5)

_ _ _ _ _ _ _ _
for the first place there are 5 letters to choose from. Lets choose N. (there are 5 ways)
N

letters : a, i, o, o, t, t, n, ( 7 letters in total but 2 are repeated) (when the repeated are not counted there is 5)


_ _ _ _ _ _ _

Lets choose N. (there are 7 ways to choose the second place)
NN

letters : a, i, o, o, t, t, ,( 6 letters in total but 2 are repeated) (when the repeated are not counted there is 4)


_ _ _ _ _ _

Lets choose A. (there are 4 ways to choose a letter for the 3rd place)
NNA

letters : i, o, o, t, t, ( 5 letters in total but 2 are repeated) (when the repeated are not counted there is 3)

Basically i continue to do this until i fill up all the places. There are 5 x 7 x 4 x 3 x 2 x 3 x 2 x 1 = 5040 ways


_ _ _ _ _

Lets choose I. (there are 3 ways to choose the 4th place)
NNAI

letters : i, o, o, t, t, ( 5 letters in total but 2 are repeated) (when the repeated are not counted there is 3)


_ _ _ _ _

for the 5th place there are 7 letters to choose from. Lets choose I. (there are 3 ways to choose the 4th place)
NNAIT
Last edited by mqb2766; 5 months ago
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DFranklin
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This should be covered in your text book. It's a "standard problem" with a formula that I believe is quotable. On the other hand, you should at least have a basic understanding of why the formula works, so I would try to find suitable examples in your text book.

If you can't get that to work, I suggest you google permutation repetition - but be aware most of the links will just quote the formula.
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bigmansouf
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(Original post by DFranklin)
This should be covered in your text book. It's a "standard problem" with a formula that I believe is quotable. On the other hand, you should at least have a basic understanding of why the formula works, so I would try to find suitable examples in your text book.

If you can't get that to work, I suggest you google permutation repetition - but be aware most of the links will just quote the formula.
(Original post by mqb2766)
A hard way to proceed because of the branching which occurs. Just go with your original 8! idea/arrangement.

If one letter is repeated (occurs twice) what would you divide the total number by?
If two letters are repeated (both occur twice) what would you divide by
... for three letters ...
This is how the textbook approach this section of the arrangement topic this way. (see attached pic)

I want to understand this method before i move on to the permutation section which is next but I will look into what you have told me thank you
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mqb2766
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I don't think that example helps much for this problem where some entries are repeated.
* If all letters were distinct there would be 8! arrangements
* If two letters are identical and the other 6 distinct there would be ... 8!/?
...
and work it up to the notation example where there are 3 pairs of repeated letters

(Original post by bigmansouf)
This is how the textbook approach this section of the arrangement topic this way. (see attached pic)

I want to understand this method before i move on to the permutation section which is next but I will look into what you have told me thank you
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ghostwalker
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(Original post by bigmansouf)
This is how the textbook approach this section of the arrangement topic this way. (see attached pic)

I want to understand this method before i move on to the permutation section which is next but I will look into what you have told me thank you
If it's the same set of notes I just dug up on the 'net, you'll find it useful to look at example 8 (using BESEIGE), three or four pages further on. I get the impression you're doing this question before you've covered the relevant material.
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bigmansouf
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(Original post by ghostwalker)
If it's the same set of notes I just dug up on the 'net, you'll find it useful to look at example 8 (using BESEIGE), three or four pages further on. I get the impression you're doing this question before you've covered the relevant material.
thanks i did look at the example 8 on page 249
the answer for this question using the permutation method is
 \frac{8!}{2! 2! 2!} = \frac{(8)(7).(6)(5)(4)(3)(2)(1)}  {(2)(1)(2)(1)(2)(1)} = (7)(5)(4)(4)(3)(3)= 5040

thank you
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