31.How many arrangements of the letters of the word ‘BENGALI’ can be made
(i) If the vowels are never together.
(ii) If the vowels are to occupy only odd places.
Solution:
There are 7 letters in the word ‘Bengali; of these 3 are vowels and 4 consonants.
(i) Considering vowels a, e, i as one letter, we can arrange 4+1 letters in 5! ways in each of which vowels are together. These 3 vowels can be arranged among themselves in 3! ways.
=> Total number of words =5!*3!
=120*6= 720
(ii) There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in P34 ways and 4 constants can be arranged in P44 ways.
=> Number of words =4P3*4P4= 576
