in how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together.

a) 360
b) 720
c) 480
d) 5040

• 720.
  
  vowels always come together therefore A, E, I are taken as ONE leter. so there are 5! ways of arranging 5 letters.
  also A, E, I can be arranged in 3!ways among themselves.
  
  so, total ways of arranging L E A D I N G = 5! * 3! = 120 * 6 = 720.
• 10 years agoHelpfull: Yes(27) No(0)
• LEADING=(LDNG)(AEI)=(5!)(3!)=720
• 10 years agoHelpfull: Yes(10) No(0)
• LDNG(EDI)
  5!*3!=120
• 10 years agoHelpfull: Yes(1) No(7)
• ans.-720
  we have to arrange he letters LDNG(EAI)..
  5 letters can be arranged in 5! ways=120..
  vowels can be arranged in 3! ways=6..
  so number of ways=120*6=720..
• 10 years agoHelpfull: Yes(1) No(0)
• 5! !3=720
  ans 720
• 10 years agoHelpfull: Yes(1) No(0)
• 5!*3!=720
  
• 10 years agoHelpfull: Yes(1) No(0)
• 5!*3!=720 ways
• 10 years agoHelpfull: Yes(1) No(0)
• There are 3 vowels so consider it as 1 word
  so 5!*3!=720
• 10 years agoHelpfull: Yes(0) No(1)
• 3 vowel arrange as 3!
  4 consonant + 1 can be arranger as 5!
  So, total no. of way= 5!*3!= 120*6= 720
• 10 years agoHelpfull: Yes(0) No(0)