Question from Perms and Combs unit

[wScott]

Homework Statement

Given the letters of the word ELEMENTS, how many 5 letter "words" can be found in which vowels and consonants alternate

Homework Equations

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?

 

[NateTG]

Is there any difference between the first and last E?

 

[wScott]

Don't think so.

 

[NateTG]

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

 

[wScott]

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

 

[arunbg]

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