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

10080

Number of letters in HARDWARE = 8 letters

Letter A repeated = 2 times

Letter R repeated = 2 times

Number of ways in which letters of word  HARDWARE  can be arranged

= \(\frac{ 8 !}{ 2! }\)

= = \(\frac{ 8×7× 6× 5 ×  4 × 3 × 2!}{ 2! × 2!  }\)

= 10080

The correct answer is option (3) : 10080