How many ways can you arrange the letters of the word hexagon such that the vowels are always together?

11. In how many ways can you arrange the letters of the word HEXAGON such that the vowels are always together?
A.
C.
B.
D.

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Answer:

720

= 6 ways. Required number of arrangements with vowels together =(120×6)=720.

The given word contains 7 letters, which may be arranged themselves in 7! = 5040 ways. <br> The given word contains 3 vowels and 4 consonants. <br> Taking the 3 vowels EAO as one letter, this letter and 4 more letters can be arranged in 5! = 120 ways. <br> The 3 vowels can be arranged among themselves in 3! = 6 ways. <br> Required number of arrangements with vowels together

=(120 xx 6)=720.