Question

Find how many words can be formed out of the letters of the word 'ORIENTAL' so that vowels always occupy the odd places.

• A. 576
• B. 578
• C. 676
• D. None of these

Answer 1

The correct option is A 576

The vowels in the word 'ORIENTAL' are: O, I, E and A
Total number of letters in the word 'ORIENTAL' = 8.
Number of vowels = 4
O R I E N T A L
1 2 3 4 5 6 7 8
X X X X
$\because$ Vowels occupy odd places, that is 1, 3, 5 and 7.
Number of odd places = 4
$\therefore$ 4 vowels can be arranged in 4 'X' marked places = P (4, 4) ways = 4! ways
Number of consonants = 4.
$\therefore$ 4 consonants can be arranged in four places
= P (4, 4) ways = 4! ways
$\therefore$ The required number of words
$=4!\times 4!=24\times 24=576.$