In how many different ways can the letters of the word 'HARDWARE' be arranged in such a way that the vowels always come together ?
Answer & explanation
Correct answer: option 3
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