[48] In how many different ways can the letters of the word JUDGE be arranged such that the vowels always

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

None of these

Explanation:

The word JUDGE has 5 letters. It has 2 vowels [UE] and these 2 vowels should always come together. Hence these 2 vowels can be grouped and considered as a single letter. That is, JDG[UE].

Hence we can assume total letters as 4 and all these letters are different. Number of ways to arrange these letters

= 4!=4×3×2×1=24

In the 2 vowels [UE], all the vowels are different. Number of ways to arrange these vowels among themselves

=2!=2×1=2

Total number of ways =24×2=48

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