Q. How many 4 digit number are there which have exactly 3 distinct digit

• 9*9*8*10
  for thousand place any digit 1-9 can be selected. for hundred place any digit 1-0 excluding the previous selected can be selected. for tens place any digit can be selected from remaining 9 and for the last any digit can be selected because 3 digit need to be distinct.
• 10 years agoHelpfull: Yes(21) No(4)
• 9*9*8*7
  ques is about no repetition.
  so first place cant be zero . first digit would b (1 to 9) so total there is 9 ways to fill first place
  second digit would be (0 to 9 but exepting one which is already set for a instance)so total ways again 9to be filled second digit.
  simillarly
  total 8 ways to fill 3rd digit
  total 7 ways to fill 4th digit
  so ultimately result is 9*9*8*7
  second digit w
• 10 years agoHelpfull: Yes(11) No(5)
• As there should be 3 distinct digits in 4, the number will have 2 same digits and other 2 distinct - aabc (1123, 3477, ...)
  
  C^3_{10}=120 - # of ways to choose 3 distinct digits out of 10;
  C^1_3=3 - # of ways to choose which digit will be represented twice;
  frac{4!}{2!}=12 - # of permutation of digits aabc;
  
  C^3_{10}*C^1_3*frac{4!}{2!}=4320.
  
  Now, out of these 4320 numbers some will start with zero, but 4-digit number can not start with zero as in this case it becomes 3 digit number. So how many out of these 4320 start with zero? As no digit has any preferences so equal numbers will start with each digit: 1/10 will start with 1, 1/10 with 2, 1/10 with 3 and so on. Thus 1/10=0.1 of 4320 will start with 0 and 0.9 of 4320 will start with digit other than zero.
  
  TOTAL: 4320*0.9=3888.
• 10 years agoHelpfull: Yes(1) No(1)
• total number of 4 digit number which is divisible by 4 ??
• 10 years agoHelpfull: Yes(0) No(0)
• exactly 3 distinct digits means we should hav only the units digit same as the remaining digits, and we should not hav even 4 distinct digits
• 10 years agoHelpfull: Yes(0) No(0)