In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A. $$\frac{{6!}}{2}$$
B. 3! × 3!
C. $$\frac{{4!}}{2}$$
D. $$\frac{{4! \times 3!}}{{2!}}$$
E. $$\frac{{5!}}{2}$$
Answer: Option D
Solution(By Examveda Team)
ABACUS is a 6 letter word with 3 of the letters being vowels. If the 3 vowels have to appear together as stated in the question, then there will 3 consonants and a set of 3 vowels grouped together. One group of 3 vowels and 3 consonants are essentially 4 elements to be rearranged. The number of possible rearrangements is 4! The group of 3 vowels contains two a s and one u The 3 vowels can rearrange amongst themselves in $$\frac{{3!}}{{2!}}$$ ways as the vowel a appears twice. Hence, the total number of rearrangements in which the vowels appear together are: $$\frac{{4! \times 3!}}{{2!}}$$This Question Belongs to Arithmetic Ability >> Permutation And Combination
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