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In how many different ways can the letters of the word JUDGE be arranged in such a way that the vowels always come together?

A) 48
B) 124
C) 120
D) 160

Correct Answer:

A) 48

Description for Correct answer:
No. of vowels in the word JUDGE = 2 i.e., U and E.

In such cases we treat the group of two vowels as one entity or one letter because they are supposed to always come together. Thus, the problem reduces to arranging 4 letters i.e. J, D. G and [UE] in 4 vacant places.

No. of ways 4 letters can be arranged in 4 places = \( \Large 4 \times 3 \times 2 \times 1 \) = 24

But the 2 vowels can be arranged among themselves in 2 different ways by interchanging their position. Hence, each of the above 24 arrangements can be written in 2 ways.

Therefore, Required No. of total arrangements = \( \Large 24 \times 2 \) = 48

Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination

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