Question

How many ways the letters of the word ORIENTAL can be arranged if no two vowels come together?

Answer 1

THERE ARE EIGHT WORDS COME IN WORD ORIENTAL with four vowels (o,i,e and a).

bunch up the four vowels to be considered as a single letter.

the total arrangements of the letters in the word oriental with the vowel always together is 20*24 equal 2880.

hope it's helpful for you

I know this answer is not perfect.

Answer 2

Number of ways when tow vowels come not together=37440

Step-by-step explanation:

There are 8 letters in word "ORIENTAL''

Therefore, total number of ways =8!=$8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320$

By using formula $n!=n(n-1)(n-2)..3\times 2\times 1$

Vowels :O,A,I,E

Number of vowels=4

Let OAIE=S

When 4 vowels come together then the word can be write as

SRNTL

Number of ways in which SRNTL can be arranged=5!

Number of ways in which 4 vowels can be  arranged=4!

Therefore,total number of ways in which word ORIENTAL can be arranged =$4!\times 5!=4\times 3\times 2\times 5\times 4\times 3\times 2\times 1=2880$

Therefore, number of ways when tow vowels come not together=40320-2880=37440

#Learns more:

https://brainly.in/question/641543