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

[Punkyc7]

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

 

[Mark44]

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)".

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

 

[Punkyc7]

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

 

[Dick]

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.

 

[Punkyc7]

ok so my answer is right, it just seem to large

 

[Dick]

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.

 

[Punkyc7]

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

 

[Dick]

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.