CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
In how many ways can the letters of the word 'MANAGEMENT' be arranged so that all the vowels come together? (Vowels: A, A, E; consonants: M, N, G, M, N, T, with M twice and N twice.)
The answer is 3780 by treating the vowels as a block, but this question has an error and should not be used.
- A15120Correct
- B30240
- C7560
- D45360
Explanation
Treat the 3 vowels A, A, E as one block. The block plus 6 consonants M, N, G, M, N, T gives 7 objects with M twice and N twice: 7!/(2!×2!) = 5040/4 = 1260. Vowels within the block can be arranged in 3!/2! = 3 ways. Total = 1260 × 3 = 3780. This does not match 15120, so the correct value is 3780, which is not listed; recompute by options given is not valid.
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