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

Options

A. 360
B. 480
C. 720
D. 5040

Answer

C

Explanation

The word 'LEADING ' has 7 different letters.
when the vowels EAI are always together , they can be supposed to form one letter.
then , we have to arrange the letters LNDG (EAI) .
Now , 5(4+1=5) letters can be arranged in 5! = 120 ways . the vowels (EAI) can be arranged among themselves in 3! = 6 ways.
`therefore ` Required number of ways `=(120 xx6)= 720`