# Question from Perms and Combs unit

1. May 14, 2007

### wScott

1. The problem statement, all variables and given/known data
Given the letters of the word ELEMENTS, how many 5 letter "words" can be found in which vowels and consonants alternate

2. Relevant equations

3. The attempt at a solution
I see the need to use Cases here because the pattern can either go:

v c v c v

or

c v c v c

So I did:

Case 1 : vowel starts 3 5 2 4 1 = 120
Case 2: consonant starts 5 3 4 2 3 = 360

Add them up to get 480, however the answer says 80. What went wrong? Or was that a typo mistake?

2. May 14, 2007

### NateTG

Is there any difference between the first and last E?

3. May 14, 2007

### wScott

Don't think so.

4. May 15, 2007

### NateTG

So how many different ways are there to arrange the vowels?

5. May 15, 2007

### wScott

Nevermind, I found out what I did wrong, I forgot to devide each case by 3! for the repetitive E's.

6. May 15, 2007

### arunbg

What do you mean "nevermind", that was what Nate was pointing out all along.