# Partition of the alphabet

1. Aug 26, 2011

### 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

2. Aug 26, 2011

### Staff: Mentor

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)".

3. Aug 26, 2011

### 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

4. Aug 26, 2011

### Dick

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. Aug 26, 2011

### Punkyc7

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

6. Aug 26, 2011

### Dick

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. Aug 26, 2011

### 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

8. Aug 26, 2011

### Dick

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.