How many different sequences of 3 letters can you make using the letters in the word "SYZYGY"?
by 
Anonymous
ANSWERS: 1
-
We can't use regular plain old combinatorics because of the three Y's. Let's consider four different cases: 3 Y's - There's only one of these, and you can't rearrange them: YYY 2 Y's - There are three other letters you can put with the Y's: S, Z, and G, and there are three positions the other letter can go, before the Y's, after the Y's, and between the Y's, for a total of 9: SYY YSY YYS ZYY YZY YYZ GYY YGY YYG 1 Y - You have to pick two of the remaining three letters to pair with the Y, and when you pick a pair there's one letter left over, so there are only three pairs: SZ, SG, and GZ. There are 3!, or six ways of arranging three letters, so that makes a total of 18: YSZ YZS SYZ SZY ZYS ZSY YSG YGS SYG SGY GYS GSY YGZ YZG GYZ GZY ZYG ZGY 0 Y's - This leaves the three other letters SZG, and once again there are 3! ways to rearrange them: SZG SGZ ZSG ZGS GSZ GZS That gives us a grand total of 1 + 9 + 18 + 6 = 34
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC