How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?

• Note: repetition is allowed!!
  1) Three digit numbers:
  The first digit can't be zero. So it has 4 chances, and the remaining two has 5 chances each. So number of 3-digit numbers are 5*5*4=100.
  2) Two digit numbers:
  The first place has 4 chances and the second one has 5. So 20 two digit numbers can be formed.
  3) One digit numbers:
  It is obvious that 5 one digit numbers can be formed.
  4) four digit numbers:
  4-a) Fix 3 in thousands place:
  we have 5 chances for the remaining three places. so we have 125 chances.
  4-b) Fix 2 in thousands place:
  The answer is the same as in the previous one!!!
  4-c) Fix 1 in thousands place:
  The answer is the same as in the previous one!!!
  4-d) Fix 4 in thousands place:
  Since the number should be less than 4300, we can't have 4 and 3 in hundreds place.
  So we have 3*5*5 chances in this case.
  Total chances so far are 100+20+5+125+125+125+75.
  As per the given conditions, total numbers are 575!!!
• 5 years agoHelpfull: Yes(13) No(0)
• we need to create positive integers upto 4299.Now, This can be divide in two ways.
  1)Thousand place can fill with 0-3
  2)Thousand place can fill with 4
  
  for Case 1: 4*5*5*5
  Thousands place can fill in 4 ways [0-1-2-3].Remaining all can fill in 5 ways.So it can fill in 4*5*5*5=500 ways
  for Case 2: 1*3*5*5
  Since we have one way to fill Thousand place i.e.., 4 -->1
  Hundred Place can fill with 3 numbers i.e., 0,1,2 -->3
  Tens and Ones Place can fill with 5 numbers -->5*5
  Total for case 2: 1*3*5*5 = 75
  
  Add Both Cases 500+75 = 575
• 5 years agoHelpfull: Yes(2) No(0)
• number less than 4300 with only digits between 0 to 4.
  now let's say abcd is number
  now for 'a' possible digits are (0,1,2,3,4)
• 5 years agoHelpfull: Yes(1) No(9)
• One easy method is to notice that there is a one-to-one correspondence between the numbers less than 4300 that can be made from the digits 0–4 and all the numbers less than 43005 in their base-5 representation. The answer is therefore 43005=4×53+3×52=575.
  Source - Quora
• 5 years agoHelpfull: Yes(1) No(0)
• 5*4*5*5
  first place, third place, fourth place occupied by any any number(0,1,2,3,4)
  but second place occupied by 4 number (0,1,2,4) except 3 (bcoz not greater than 4300)
• 5 years agoHelpfull: Yes(0) No(7)