Question

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 1

If the word 'hardware' is to be arranged in such a way that the vowels always come together, then it can be arranged in 18 different ways 

Answer 2

4320

Explanation:

• According to the question There are 8 letters in the word ‘HARDWARE’
• There are three vowels and five consonant present in word HARDWARE
• We can arrange vowel as ( A,A,E) and consonant as  (H,R, D, E, W, R, E) .
• According to the question when the vowel comes together and form one letter the letter is A, A, E
• When we have to arrange letter HRDWRE  (AAE)
• Now, 6  letter can be arranged in 6!= 720 ways.
• The vowel AAE  can be arranged among themselves in 3! = 6 way
• Now, the Required number of way is  720 x 6 = 4320 .