How many 8 letter words have 3 vowels constants do not repeat.
Don't you have to also factor in order too:
act vs cat vs some nonsense words like tca, cta ...
cafe vs face
Another question how do I know when to use the combination equation or permutation equation?
For instance given the example which is posted above are the following strings the same?
A E I M N P Q R
E A I M N P Q R
They both contain the same three vowels and the only thing I changed was the placement of the first and second terms
so I should add 8! ?
I'm not sure that would work, for instance
A1 B A2
A2 B A1
are the same.
I almost feel like I should add (8 choose 3) instead of 8!
I think your consonants are unique but your vowels might repeat so you'd also have to factor that in too.
You mean multiply by 8!?
No, your original formula already has some ordering in it.
For the vowels you have 53, so you've already counted all vowel orders.
Similarly, for the consonants, you used 26P5, not 26C5, so you have those ordered.
All that you are missing is integrating the vowels with the consonants. How many ways are there of doing that?
Remember that the vowels are part of the 26 letters. There are only 21 consonants.
I missed that, thanks.
Separate names with a comma.