# Counting question

1. Dec 10, 2013

### Miike012

How many 8 letter words have 3 vowels constants do not repeat.

Is it
5^3*26*25*24*23*22 ?

2. Dec 10, 2013

### Staff: Mentor

Don't you have to also factor in order too:

act vs cat vs some nonsense words like tca, cta ...

cafe vs face

3. Dec 10, 2013

### Miike012

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
and
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

4. Dec 10, 2013

### Miike012

so I should add 8! ?

5. Dec 10, 2013

### Miike012

I'm not sure that would work, for instance

A1 B A2
and
A2 B A1

are the same.

I almost feel like I should add (8 choose 3) instead of 8!

6. Dec 10, 2013

### Staff: Mentor

I think your consonants are unique but your vowels might repeat so you'd also have to factor that in too.

7. Dec 11, 2013

### haruspex

You mean multiply by 8!?
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?

8. Dec 11, 2013

### vela

Staff Emeritus
Remember that the vowels are part of the 26 letters. There are only 21 consonants.

9. Dec 11, 2013

### Staff: Mentor

I missed that, thanks.

10. Dec 11, 2013

How true