SOLUTION: If a permutation of the word "white" is selected at random, find the probability that has the consonants and vowels alternating.

They can only be in this form CVCVC, where C is a consonant 
and V is a vowel.

Choose a consonant to go first any of 3 ways, W,H, or T
That leaves 2 ways to choose a consonant to go third.
That leaves 1 way to choose a consonant to go fifth.
Choose a vowel to go second either of two ways, I or E.
That leaves 1 vowel to go fourth.

Answer 3*2*1*2*1 = 3!2! = 6*2 = 12 ways

 1. WIHET
 2. WEHIT
 3. WITEH
 4. WETIH
 5. HIWET
 6. HEWIT
 7. HITEW
 8. HETIW
 9. TIWEH
10. TEWIH
11. TIHEW
12. TEHIW

Edwin