Question #36b06

1 Answer
Dec 5, 2017

a. #12# ways

Explanation:

Given: WHITE, alternate consonants and vowels

There are 3 consonants and 2 vowels. This means we must start with a consonant to alternate.

There are 3 possible consonants for the 1st letter.

There are 2 possible vowels for the 2nd letter.

Since we used one consonant for the 1st letter, there are only 2 consonants left to use for the 3rd letter.

Since we used one vowel for the 2nd letter, there is only one vowel left to use for the 4th letter.

Since we used one consonant for the 1st letter, and one for the 3rd letter, there is only one consonant left to use for the 5th letter.

#3 * 2 * 2 * 1 * 1 = 12# ways

Here is the set of all words where we alternate consonants and vowels: {WIHET, WITEH, WEHIT, WETIH, HITEW, HIWET, HETIW, HEWIT, TIHEW, TIWEH, TEHIW, TEWIH}