In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always… · ABC26GN5327
Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: DMRC—Train Operator/Station Controller Exam 2016
In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?
(a)2429500
(b)1360800
(c)1627800
(d)None of these
Answer
Answer (as printed): B
Explanation
The word TRANSPIRATION has 13 letters in which each of T, R, A, N and I has come two time We have to arrange TT RR NN PS (AA II O). There are five vowels in the given words. ∴ we consider these give vowels as one letter. ∴ Required number of arrangements. 9! × 5! = 2!2!2!2!2! 9×8×7 ×6× 5× 4× 3× 2× 5× 4× 3× 2 = 2×2×2×2×2 = 1360800
Explanation as extracted from the printed page; notation may be imperfect.