Arithmetic Ability
Permutations and Combinations

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Q.

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

View Answer

Correct choice: C

Explanation:

ABACUS is a 6 letter word with 3 of the letters being vowels. If the 3 vowels have to appear together, then there will 3 other consonants and a set of 3 vowels together. These 4 elements can be rearranged in 4! Ways. The 3 vowels can rearrange amongst themselves in 3!/2! ways as "a" appears twice. Hence, the total number of rearrangements in which the vowels appear together are (4! x 3!)/2!
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