# Thread: combinatorics - combination & permutation?

1. ## combinatorics - combination & permutation?

How many words can be made using the letters of the word SYZYGY? (words of abitrary lengths is allowed)

I understand that for at most one Y, so thess are the words made out of SYZG, the number of ways of doing it is 65

but then I dunno how to find the rest,,

can someone explain it please?

The answer is:

Two Ys $((3C0)2!+(3C1)3!+(3C2)4!+(3C3)5!)/2=106$

With All Three Ys $((3C0)3!+(3C1)4!+(3C2)5!+(3C3)6!)/3!=193$

Adding the sum together: $65+106+193=364$

Thanks!

2. Originally Posted by sofialam
How many words can be made using the letters of the word SYZYGY? (words of abitrary lengths is allowed)

I understand that for at most one Y, so thess are the words made out of SYZG, the number of ways of doing it is 65

but then I dunno how to find the rest,,

can someone explain it please?

The answer is:

Two Ys $((3C0)2!+(3C1)3!+(3C2)4!+(3C3)5!)/2=106$

With All Three Ys $((3C0)3!+(3C1)4!+(3C2)5!+(3C3)6!)/3!=193$

Adding the sum together: $65+106+193=364$

Thanks!
I don't understand the question. If words of arbitrary length are allowed then there are an infinite number of words.

3. oh! umm.. then each letter can only use once, so the longest length would be 6.