How many different ways can the letters in the word 'DETAIL' be arranged so that the vowels only appear in odd positions?
A. 32
B.48
C. 36
D. 60
Answer:C
How many different ways can the letters in the word 'DETAIL' be arranged so that the vowels only appear in odd positions?
A. 32 B.48 C. 36 D. 60
Explanation: There are six letters in the given word, three vowels and three consonants.Let's label these areas as follows:(1) (2) (3) (4) (5) (6) (7) (8) (8) (8) (8) (8) (6),Three vowels can now be put in any of the three spaces marked 1, 3, and 5.The number of different ways to arrange the vowels is 3P3 = 3! = 6.The three consonants can also be placed in any of the other three slots.The number of different ways these configurations may be made is 3P3 = 3! = 6.The total number of ways is 36 (6 × 6).