How many 4 digit numbers can be made by using digits 1 to7(repetition is not allowed),if the digit 4 will always be there in the number?

a. 400
b. 480
c. 360
d. 240
e. None of these

• Ans: 480
  Place 4 in all the four places one by one and arrange the rest.
  4 _ _ _ = 1*6*5*4 = 120
  _ 4 _ _ = 6*1*5*4 = 120
  _ _ 4 _ = 6*5*1*4 = 120
  _ _ _ 4 = 6*5*4*1 = 120
  
  Total = 120*4= 480.
• 10 years agoHelpfull: Yes(37) No(1)
• Ans 480
  4 digit no to be formed using digits from 1 to 7 without repetition with 4 always included in the no
  So we can place the digit 4 in the no in 4 ways
  Remaining 6 digits need to be placed in the remaining 3 places without repetition that can be done in 6p3 ways
  Therefore 6p3*4=6*5*4*4=480
  
• 10 years agoHelpfull: Yes(9) No(2)
• at unit place take 4 then total no=1*6*5*4=120
  in this way 4 can occur at ten's place thousand;s place ,ten thousand's place
  so there will be total 4*120 arrangement
  so no=480.
• 10 years agoHelpfull: Yes(4) No(1)
• Ans : b)480
  Since the digit 4 should be there in the no.,considering 4 at first units place,
  the next place can have any digit from 1-7 other than 4 ;so 6 cases.
  For each of these 6 cases, the next place can take any of the existing 5.And thus 6*5 cases.Like wise keeping 4 at units place there can be 6*5*4 = 120 possibilities.Similarly placing 4 at other 3 places,we get 4*120 = 480 no.s in total.
• 10 years agoHelpfull: Yes(1) No(0)
• digit 4 is fixed...so for rest 3 digits we have 6 possible options without reptitation....that makes it 6c1*5c1*4c1=120.
  Now the digit 4 can be placed in 4 ways, so its 4*120=480(opt B)
• 10 years agoHelpfull: Yes(1) No(0)
• Ans: 480
  Place 4 in all the four places one by one and arrange the rest.
  4 _ _ _ = 1*6*5*4 = 120
  _ 4 _ _ = 6*1*5*4 = 120
  _ _ 4 _ = 6*5*1*4 = 120
  _ _ _ 4 = 6*5*4*1 = 120
  
  Total = 120*4= 480.
• 10 years agoHelpfull: Yes(1) No(0)
• 4*(6*5*4)=480
• 10 years agoHelpfull: Yes(0) No(0)
• ans...120
  
• 10 years agoHelpfull: Yes(0) No(7)
• ans 480
  4*6*5*4=480
• 10 years agoHelpfull: Yes(0) No(1)
• Ans: 600
  total digits=7
  let us consider 4 occupies the 1st position then the possible chance is
  4_ _ _
  1*6*5*4=150
  but 4 may come in 2 or 3 or 4th place.so 150*4=600
• 10 years agoHelpfull: Yes(0) No(5)
• Ans 480
  total digits=7
  let us consider 4 occupies the 1st position,
  4_ _ _
  1*6*5*4=120
  Now 4 will similarly occupy 2nd,3rd & 4th position as well,and the calculation remains the same,
  so, for all 4 cases, 4*(6*5*4) = 480
• 10 years agoHelpfull: Yes(0) No(0)