In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come… · ABC26GN5320
Subject: General Aptitude · Chapter: Permutations and Combinations
In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come together?
(a)10080
(b)120960
(c)4989600
(d)20160
(e)None of these
Answer
Answer (as printed): B
Explanation
Keeping the vowels (AEIA) together, we have MTHMTCS(AEAI). Now, we have to arrange 8 letters, out of which we have 2M, 2T and the rest are all different. Number of ways of arranging these letters 8 8×7 ×6×5×4×3×2×1 = = = 10080.
Explanation as extracted from the printed page; notation may be imperfect.