Hi, I'm just looking for some different ways to solve this.
How many different arrangements of the letters SPECIAL can be made using exactly 2 vowels and exactly 2 consonants?
Thanks in advance! < 3
Hey Pourdo.
Your question is a little bit ambiguous since having only 2 vowels and 2 constants means that you aren't just re-arranging the words but creating a word which has a subset of symbols.
Are you trying to just find the number of ways of creating a new word with two vowels and two consonants?
Hmm sorry if it was confusing. Yes I believe it is asking how many 4 letter arrangements you can create using the letters S P E C I A L but the 4 letter arrangements must have two vowels and two consonants.
Vowels - E I A
Consonants - S P C L
Are you aware of the hyper-geometric distribution?
Hypergeometric distribution - Wikipedia, the free encyclopedia
Hello, Pourdo!
I would solve it like this . . .How many different arrangements of the letters SPECIAL can be made
using exactly 2 vowels and exactly 2 consonants?
There are 3 vowels:.$\displaystyle \{A,E,I\}$
There are 4 consonants:.$\displaystyle \{C,L,P,S\}$
Select 2 vowels: $\displaystyle {3\choose2} = 3$ ways.
Select 2 consonants: $\displaystyle {4\choose2} = 6$ ways.
Arrange the 4 letters: $\displaystyle 4! = 24$ ways.
Therefore:. $\displaystyle 3\cdot6\cdot24 \,=\,432$ arrangements.