How do I find the number of partitions of the alphabet?

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In summary, the conversation discusses finding the number of partitions of the alphabet {A,b...Z} of the type (2,2,2,3,3,3,3,4,4). After performing calculations, the speaker confirms that the obtained number, 234481761013500000, is correct. They also mention that this type of combinatorial problem often results in very large numbers, even for small sets of elements.
  • #1
Punkyc7
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Find the number of the partition of the alphabet {A,b.....Z} of the type (2,2,2,3,3,3,3,4,4)


So I did 26!/(2!2!2!3!3!3!3!4!4!) = A REALLY BIG NUMBER

then I took that number and dived it by (3!4!2!) and got 2.344 x10^17 which seems to big to be an answer. So I'm wondering if the number should be that big or did I mess up somewhere
 
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  • #2
Punkyc7 said:
Find the number of the partition of the alphabet {A,b.....Z} of the type (2,2,2,3,3,3,3,4,4)
Shouldn't B be in the alphabet, not b?

Please clarify what you mean by the terms "number of the partition of the alphabet " and "of the type (2,2,2,3,3,3,3,4,4)".
Punkyc7 said:
So I did 26!/(2!2!2!3!3!3!3!4!4!) = A REALLY BIG NUMBER

then I took that number and dived it by (3!4!2!) and got 2.344 x10^17 which seems to big to be an answer. So I'm wondering if the number should be that big or did I mess up somewhere
 
  • #3
yes b is B sorry about that is all 26 of them

(2,2,2,3,3,3,3,4,4)

means like AB| CD| EF | GHI|...|WXYZ
 
  • #4
Punkyc7 said:
yes b is B sorry about that is all 26 of them

(2,2,2,3,3,3,3,4,4)

means like AB| CD| EF | GHI|...|WXYZ

You should expect to get a really large number. There are lots splitting the alphabet into groups like that. I get the same number, 234481761013500000, if you want to spell it out exactly.
 
  • #5
ok so my answer is right, it just seem to large
 
  • #6
Punkyc7 said:
ok so my answer is right, it just seem to large

Just out of curiosity, how large would you think it ought to be? I would expect something in the rough ballpark of 26!. And that's similarly large.
 
  • #7
I understand that 26! is large. I was thinking that I must have messed up somewhere when dividing by using the wrong number or something
 
  • #8
Punkyc7 said:
I understand that 26! is large. I was thinking that I must have messed up somewhere when dividing by using the wrong number or something

No mess up. Good job. Just adjust your intuition. Combinatorial answers to questions with even smallish number of element (like 26) often give huge answers.
 

1. What is the partition of the alphabet?

The partition of the alphabet refers to the division of the 26 letters of the English alphabet into smaller groups or subsets based on specific criteria or patterns.

2. What are the different ways to partition the alphabet?

There are many ways to partition the alphabet, such as by vowel and consonant, by alphabetical order, by frequency of use, by phonetic sound, by handwriting strokes, etc.

3. Why is the partition of the alphabet important?

The partition of the alphabet can be useful for organizing and categorizing letters in various contexts, such as language learning, coding and programming, data analysis, and more.

4. How does the partition of the alphabet vary across different languages?

The partition of the alphabet can vary significantly across different languages, as each language may have a different number of letters, different sounds and phonetics, and different writing systems.

5. Can the partition of the alphabet change over time?

Yes, the partition of the alphabet can change over time as languages evolve and new writing systems are developed. It can also be influenced by cultural and societal changes.

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