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
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
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:.
There are 4 consonants:.
Select 2 vowels: ways.
Select 2 consonants: ways.
Arrange the 4 letters: ways.