SOLUTION: Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if: the first letter must be Y the vowels and consonants alternate, beginning

Algebra ->  Permutations -> SOLUTION: Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if: the first letter must be Y the vowels and consonants alternate, beginning      Log On


   

Question 85123: Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
the first letter must be Y
the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are 120 different combinations with these letters. This list was generated by a program, but there is a much easier way to calculate the number of combinations. If you have five unique letters, then the number of possible combinations is

5%21=5%2A4%2A3%2A2%2A1=120 which is read as 5 factorial
but if you're curious, here's the list of all possible combinations (the letters do not repeat)

YOUNG
YOUGN
YONUG
YONGU
YOGUN
YOGNU
YUONG
YUOGN
YUNOG
YUNGO
YUGON
YUGNO
YNOUG
YNOGU
YNUOG
YNUGO
YNGOU
YNGUO
YGOUN
YGONU
YGUON
YGUNO
YGNOU
YGNUO
OYUNG
OYUGN
OYNUG
OYNGU
OYGUN
OYGNU
OUYNG
OUYGN
OUNYG
OUNGY
OUGYN
OUGNY
ONYUG
ONYGU
ONUYG
ONUGY
ONGYU
ONGUY
OGYUN
OGYNU
OGUYN
OGUNY
OGNYU
OGNUY
UYONG
UYOGN
UYNOG
UYNGO
UYGON
UYGNO
UOYNG
UOYGN
UONYG
UONGY
UOGYN
UOGNY
UNYOG

UNYGO
UNOYG
UNOGY
UNGYO
UNGOY
UGYON
UGYNO
UGOYN
UGONY
UGNYO
UGNOY
NYOUG
NYOGU
NYUOG
NYUGO
NYGOU
NYGUO
NOYUG
NOYGU
NOUYG
NOUGY
NOGYU
NOGUY
NUYOG
NUYGO
NUOYG
NUOGY
NUGYO
NUGOY
NGYOU
NGYUO
NGOYU
NGOUY
NGUYO
NGUOY
GYOUN
GYONU
GYUON
GYUNO
GYNOU
GYNUO
GOYUN
GOYNU
GOUYN
GOUNY
GONYU
GONUY
GUYON
GUYNO
GUOYN
GUONY
GUNYO
GUNOY
GNYOU
GNYUO
GNOYU
GNOUY
GNUYO
GNUOY