# 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?

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?

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: $65+106+193=364$