Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:
In how many different ways can the letters of the word MACHINE be arranged so that the vowels may occupy only the odd positions?
(a)210
(b)576
(c)144
(d)1728
(e)3456
Answer
Answer (as printed): B
Explanation
There are 7 letters in the given word, out of which there are 3 vowels and 4 consonants. Let us mark the positions to be filled up as follows: (1)(2)(3)(4)(5)(6)(7) Now, 3 vowels can be placed at any of the three places out of four marked 1, 3, 5, 7. Number of ways of arranging the vowels = 4P3 = (4 × 3 × 2) = 24. 4 consonants at the remaining 4 positions may be arranged in 4P4 = 4 = 24 ways. Required number of ways = (24 × 24) = 576.
Explanation as extracted from the printed page; notation may be imperfect.