Question

How many arrangements of the letters of the word OREINTAL can be made so that there are no restrictions​

Answer 1

Answer:

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

Answer 2

Answer:

There are 8 letters in the word oriental with 4 vowels (o,i,e and a). All possible arrangements of these 8 letters is 8!=40320 . Now, bunch up the 4 vowels to be considered as a single letter. Then, the number of letters in the word becomes 5 which can be arranged in 5!=120 ways. Again, these 4 vowels can be arranged among themselves in 4!=24 ways. So, total arrangements of the letters in the word oriental with the vowels always together is 120∗24=2880 . Hence, number of arrangements of the letters so that no two vowels will come together is 40320−2880=37440