Find The Sum Of All 4-Digit Numbers, that can be formed from the digits 0,1,3,4,5 without repetition.
a)259974
b)337974
c)346632
d)334554

• it's very simple.
  n=5 i.e 0,1,3,4,5
  1.for thousandth position we can use only 1,3,4,5.(can not use 0)
  add numbers i.e 1+3+4+5=13
  thousandth position sum=1000*13*(n-1)!=1000*13*24
  
  2.hundredth position sum=100*13*(n-1)!=100*13*24
  
  3.tenth position sum=10*13*(n-1)=10*13*24
  
  4.unit position sum=1*13*24
  
  5.13*24=312
  
  6.so sum of all 312(1000+100+10+1)
  i.e 312*1111
  =346632
  i.e option c
  thank you
  
• 10 years agoHelpfull: Yes(19) No(1)
• b)337974
  Trying to explain sol of DIPIN.
  Total 96 numbers can be formed.
  No number can start with 0.
  no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
  when no is starting with 1,
  0,3,4,5.. each number will appear in unit place 6 times.
  so (0+3+4+5)*6 = 72
  when no is starting with 3,
  0,3,4,5.. each number will appear in unit place 6 times.
  so (0+1+4+5)*6 = 60
  when no is starting with 4,
  0,3,4,5.. each number will appear in unit place 6 times.
  so (0+3+1+5)*6 = 54
  when no is starting with 5,
  0,3,4,5.. each number will appear in unit place 6 times.
  so (0+3+4+1)*6 = 48
  
  sum of digits at unit place of all numbers = 234
  sum of digits at tens place of all numbers = 234
  sum of digits at hundreds place of all numbers = 234
  
  sum of digits at thousands place of all numbers = 312
  
  adding these values, we get the sum all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 3579974.
• 12 years agoHelpfull: Yes(14) No(3)
• 337974
  
  Taking help of solution given by shikha,
  
  Total 96 numbers can be formed.
  No number can start with 0.
  no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
  
  sum of digits at unit place of all numbers = 234
  sum of digits at tens place of all numbers = 234
  sum of digits at hundreds place of all numbers = 234
  
  sum of digits at thousands place of all numbers = 312
  
  considering this , sum of all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 337974
• 12 years agoHelpfull: Yes(13) No(10)
• @ Anup,
  
  I think it is well explained by Dimple and Dipin.
  
  b)337974 should be correct.
  Trying to explain sol of DIPIN and Dimple.
  Total 96 numbers can be formed.
  No number can start with 0.
  no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
  when no is starting with 1,
  0,3,4,5.. each number will appear in unit place 6 times.
  so sum of digits at unit place =(0+3+4+5)*6 = 72
  when no is starting with 3,
  0,1,4,5.. each number will appear in unit place 6 times.
  so sum of digits at unit place=(0+1+4+5)*6 = 60
  when no is starting with 4,
  0,3,1,5.. each number will appear in unit place 6 times.
  so sum of digits at unit place=(0+3+1+5)*6 = 54
  when no is starting with 5,
  0,3,4,1.. each number will appear in unit place 6 times.
  sosum of digits at unit place = (0+3+4+1)*6 = 48
  
  sum of digits at unit place of all numbers = 234
• 12 years agoHelpfull: Yes(4) No(2)
• Simple Formula = n!*(Sum of Given Digits)* (1111 for 4 digit 111 for 3 digit).
  for given situation n = 4, sum of digit = 0+1+3+4+5 = 13.
  sum = 4! (13) * (1111) = 346634
• 10 years agoHelpfull: Yes(2) No(0)
• dipin can u explain how this
  sum of digits at units palce of all nos=234
• 12 years agoHelpfull: Yes(1) No(3)
• Total 96 numbers can be formed.
  No number can start with 0.
  no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
  
  sum of digits at unit place of all numbers = 234
  sum of digits at tens place of all numbers = 234
  sum of digits at hundreds place of all numbers = 234
  sum of digits at thousands place of all numbers = 234
  sum of digits at ten thousands place of all numbers = 312
  
  considering this , sum of all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 3579974
• 12 years agoHelpfull: Yes(0) No(4)
• Dipin please explain
• 12 years agoHelpfull: Yes(0) No(2)