How many six digit phone numbers can you frame using the digits from 0 to 9 if a condition restricts you to start the number with 35 and another condition restricts you from using any digit more than once?

• ans :1680
  as the first two digits are fixed and on remaining 4places we can use only one at a time.this means on third place we can use any digit from 0,1,2,4,6,7,8,9. which means we can choose any of 8digits. similarly on 4th place any 7digits n so on..
  thus 1*1*8*7*6*5=1680
• 10 years agoHelpfull: Yes(29) No(3)
• It's a permutation question.
  there are totally 10 numbers and in which 3 and 5 are already fixed as first two digits.
  
  hence total numbers n=8
  
  and the remaining digits which are needed to be formed its 4 digits apart from the first two digits already formed in the 6 digit phone number.
  
  so r=4
  
  permutation formula npr=n!/(n-r)!
  
  =8!/4!
  =8*7*6*5*4*3*2*1/4*3*2*1
  =8*7*6*5
  =1680
• 10 years agoHelpfull: Yes(10) No(1)
• reqd no. = total no. formed - numbers starting from 35
  =10*9*8*7*6*5-8*7*6*5
  =8*7*6*5*(90-1)
  =149520
• 10 years agoHelpfull: Yes(8) No(13)
• ans will be 1680.
• 10 years agoHelpfull: Yes(5) No(1)
• Question clearly likhna chahiye na ki strt 3 ya 5 se ni hona chahiye..
  In that case..
  First digit is any from the remaining 8 and in 2nd place there are chance of 9 digits to come then in next place 8 and so on..
  (8×9×8×7×6×5) = 120960
• 10 years agoHelpfull: Yes(4) No(2)
• The first two digits are fixed.
  You are left with eight digits (since one digit can be used just once).
  Also you have only 4 more digits left to frame a phone number.
  
  Thus the possibilities = 8P4 = 1680.
• 10 years agoHelpfull: Yes(4) No(1)
• Starting 2 digits are fixed 3 and 5.
  And no any digit repeated we have also use 2 digits so 8 are remaining for 4 places.
  So ans should be (8×7×6×5) = 1680
• 10 years agoHelpfull: Yes(3) No(1)
• don't get confused friends, what rakesh said is the right answer .
  because the number can start by 32 or 33...
  the easy method would be subtracting it from total
  as per below
  reqd no. = total no. formed - numbers starting from 35
  =10*9*8*7*6*5-8*7*6*5
  =8*7*6*5*(90-1)
  =149520
• 10 years agoHelpfull: Yes(3) No(2)
• first we have to calculate the conditon that it starts with 35 so its given as 1*1*8*7*6*5=1680
  then we have to find 10*9*8*7*6*5
  and the answer is 10*9*8*7*6*5-1680=149520
  
• 10 years agoHelpfull: Yes(3) No(1)
• total six digit numbers is : 10*9*8*7*6*5 = 151200
  
  the number of six digit numbers that starts with 35 without repetition is : 1680
  
  so the numbers starting without 35 : 151200 - 1680 = 149520
• 10 years agoHelpfull: Yes(1) No(0)
• The first two number should start with 35...
  The digits should not repeat...and their will be only remaining 8 nos...
  We should decrease one digit for each next position,because the numbers should not repeat again...
  =35----
  =35(8*7*6*5)
  =(8*7*6*5)
  =1680
• 10 years agoHelpfull: Yes(1) No(0)
• two digits fixed so we need 4 digits..from 0to9 .in that two were fixed so
  (10-2)=8 . therefore we need to select 4 from 8
  npr=8p4=1680.
• 10 years agoHelpfull: Yes(1) No(0)
• please explain navin?
• 10 years agoHelpfull: Yes(0) No(0)
• Hi..Rakesh...I am also this answer only...Can i have ur mail id plz?
• 10 years agoHelpfull: Yes(0) No(3)
• @UMANG AGARWAL
  QUESTION IS RESTRICT TO TO START WITH 35.. SOANSWER IS 149520
• 10 years agoHelpfull: Yes(0) No(1)
• 
  6 digit number=abcdef
  ab is always 35
  so 35cdef
  
  8*3!+7*2!+6*1+5*0!= 48*14*6*5
• 10 years agoHelpfull: Yes(0) No(2)
• first two digits are fixed and digits are not repeated so remaining 4 places are filled with 8 digits so 8p4=1680
• 10 years agoHelpfull: Yes(0) No(1)
• let the 6 digit num be 35abcd . then the left out num are 0 1 2 4 6 7 8 9.
  In this 8 num ab can have 56 possibilities ie: out of 8 numbers possible pair combinations are 8*7=56; if we take out 2 num in this 8 coz nums cannot be repeated ,the cd can occupy 30 possibilities ,ie: 6* 5= 30
  
• 10 years agoHelpfull: Yes(0) No(1)
• 3*5*8*8*8*8=61440
• 10 years agoHelpfull: Yes(0) No(1)
• we need to form six digit number
  _ _ _ _ _ _.
  with condition of non repeating and starts with 35 so the number must be
  3 5 _ _ _ _ .
  from 0 to 9 already we used 3 and 5, the remaining numbers are 0,1,2,4,6,7,8,9, totally 8 numbers. so we have remaining four dash filled by these 8 numbers only so 8*7*6*5= 1680 is the answer.
• 10 years agoHelpfull: Yes(0) No(1)
• The 1st 2 digits are fixed.. so we can leave these terms..
  The next 4 digits can be formed from numbers 0,1,2,4,6,7,8,9..
  so if the 3rd position can be occupied by a number form the 8 numbers, the 4th position will be occupied by a number from the remaining 7 after filling 3rd position and so on
  So the answer is 8*7*6*5 = 1680
• 10 years agoHelpfull: Yes(0) No(1)
• 1680 using permutation concept to order the remaining 4 no using 8P4=1680.
  
• 10 years agoHelpfull: Yes(0) No(1)
• It is a permutation question since we are talking about ordering of numbers which should not repeat.
  Formula is nPr = n!/(n-r)!
  n - number of unique values to be chosen from. Here they are 0,1,2,4,6,7,8,9 which is 8
  r - number of values to be formed using "n" which is 4
  n is 8 because we have already used 3 and 5
  r is 4 because already first two digits are filled with 3 and 5 respectively
  
  P = 8!/4! = 40320/24 = 1680
• 10 years agoHelpfull: Yes(0) No(1)
• 8*8*8*7*6*5-1680=107520
• 9 years agoHelpfull: Yes(0) No(2)