How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (y is considered a consonant)?

The 21 consonants are :

b c d f g h j k l m n p q r s t v w x y z

The 5 vowels are :

a e i o u

Now, to arrange the consonants there are 21! ways.

Now the vowels can be arranged in 22 ways because one vowel can be placed before 'b' and one after 'z' also.

It can be shown like this : (V represents vowels)

V b V c V d V f .......................

Therefor the ways to put vowels will be :

The complete order to place consonants without repeating vowels becomes:

answer: x=3 and y=4

step-by-step explanation: