Let be an alphabet, and let n_i denote the number of appearances of

letter a_i in a word. How many words of length n in the alphabet A are there for which

and is even?

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- October 21st 2012, 03:18 PMmaximus101Combinatorics QUESTION
Let be an alphabet, and let n_i denote the number of appearances of

letter a_i in a word. How many words of length n in the alphabet A are there for which

and is even? - October 21st 2012, 03:25 PMskeeterRe: Combinatorics QUESTION
this is not calculus ... thread moved to Discrete Math

- October 21st 2012, 04:58 PMjohnsomeoneRe: Combinatorics QUESTION
"let n_i denote the number of appearances of letter a_i in a word"? Which word? Are you saying that there's a single unknown-yet-fixed word in the alphabet A which defined the numbers

OR, are you treating as k distinct functions functions from the domain of all possible finite words in A into the non-negative integers?

I would guess the later, but I'm not sure.

With that assumption:

For the middle example: imagine there are 10 slots, numbered 1 through 10, that you need to fill with those letters to make your word. Choose 5 slots to fill with the A's, and then, from the 5 remaining slots, choose 2 to fill with the B's (Obviously the rest are then filled in with C's.) The number of ways to do that will be the number of distinguishable length 10 words using 5 A's, 2 B's and 3 C's.