In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?	Answers:
A) 120
B) 190
C) 250
D) 370
E) 720
The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).   Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters   =5!=5×4×3×2×1=120   In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves   =3!=3×2×1=6=3!=3×2×1=6   Hence, required number of ways=120×6=720   Answer: 720
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In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?