how many no can be formed using digits (1,2,3,4,5,6,7,8,9)..such that they are in increasing order
(eg:0 12345,345,6789,123456789)?

• ans-->502
  sol url---> http://postimg.org/image/8buhq4q2h/
• 9 years agoHelpfull: Yes(60) No(19)
• Examples they have provided adding another angle in this question that numbers should be consecutive also. If that's the case then:
  2 digit pairs with increasing and consecutive numbers : 8
  3 digit pairs with increasing and consecutive numbers : 7
  4 digit pairs with increasing and consecutive numbers : 6
  5 digit pairs with increasing and consecutive numbers : 5
  6 digit pairs with increasing and consecutive numbers : 4
  7 digit pairs with increasing and consecutive numbers : 3
  8 digit pairs with increasing and consecutive numbers : 2
  9 digit pairs with increasing and consecutive numbers : 1
  which is equal to 36.
• 9 years agoHelpfull: Yes(24) No(7)
• 2 digit no.- 8 (12,23,34,45,56,67,78,89)
  3 digit no.- 7(123,234,345,456,567,678,789),
  4 digit no.- 6, 5 digit no -5, 6 digit no -4, 7 digit no-3, 8 digit no-2, 9 digit no -1(123456789) ,... So total =1+2+3+•••+8=36
• 9 years agoHelpfull: Yes(11) No(3)
• one can choose either on 1 digit , 2 digits 3digits ........ so on till 9 digits.
  Now correspondingly each of the above case unfolds as 9C1 , 9C2 , 9C3 and so on till 9C9.
  Since only 1 arrangement in each case is possible (that of the increasing order) thus final answer is
  9C1 + 9C2 + 9C3 + ....... + 9C9 = 2^9 -1 = 512 -1 = 511
• 8 years agoHelpfull: Yes(6) No(5)
• numbers like - 267 , or 389, 16789, 589 will not be accepted .. But numbers like 123, 567,6789,3456789 would be accepted ..
  Clearly the numbers with digits in increasing order where they are in a.p. With r=1 ..
  If it's a 5 digit no and no starts with 5 , then the number would be 56789 .
  one digit numbers would not be considered.
  2 digit no.- 8 (12,23,34,45,56,67,78,89)
  3 digit no.- 7(123,234,345,456,567,678,789),
  4 digit no.- 6, 5 digit no -5, 6 digit no -4, 7 digit no-3, 8 digit no-2, 9 digit no -1(123456789) ,... So total =1+2+3+•••+8=36
• 8 years agoHelpfull: Yes(4) No(0)
• what is the correct ans?
  
• 9 years agoHelpfull: Yes(3) No(0)
• numbers starting from 1= 8, 12=7, 123=6,...12345678=1.similarly starting from 2=7, 23=6,...2345678=1.similarly we can find from 3,4,5,6,7 and 8.observing this we obtain formula [(n-1)+...+3+2+1]+[(n-1-1)+...+3+2+1]+[(n-3)+...+3+2+1].answer is 120
• 9 years agoHelpfull: Yes(2) No(16)
• 2 digit-8
  3 digit-7
  4 digit-6
  5digit-5
  6 digit-4
  7digit-3
  8digit-2
  9digit-1
  total no of possiblity in increasing order-36
• 9 years agoHelpfull: Yes(2) No(0)
• Including single digits is not what defined as per the question.so, we shall include numbers from 2 digits to possible values of 9 digits.
  2 digit numbers to be 8 possibilities.
  3 digit numbers to be 7 possibilities.
  4 digit numbers to be 6 possibilities.
  5 digit numbers to be 5 possibilities.
  6 digit numbers to be 4 possibilities.
  7 digit numbers to be 3 possibilities.
  8 digit numbers to be 2 possibilities.
  8 digit numbers to be 1 possibilities.
  Hence total possibilities = 8+7+6+5+4+3+2+1=36.
  This must be the answer.
  but if some possibilities are introduced such as 246, 356, 237... they can also be included since as per the question they are also increasing numbers because its not mentioned that they have to be consecutive.
  
• 8 years agoHelpfull: Yes(2) No(2)
• two digit-6
  three digit-7
  four digit-6
  five digit-5
  six digit-4
  seven-3
  eight-2
  nine-1
  total=34
• 9 years agoHelpfull: Yes(1) No(13)
• @Naveen single digit no.s include kar le
• 9 years agoHelpfull: Yes(1) No(5)
• @ DYTORT tum apna ans me single digit include kr lena.....don't suggest me...
• 9 years agoHelpfull: Yes(1) No(3)
• given digits 1,2,3......9
  9c9=1
  9c8=9
  9c7=36
  9c6=84
  9c5=126
  9c4=126
  9c3=84
  9c2=36
  9c1=1
  totsl nos=(1+9+36+84+126+126+84+36+1)=503
• 8 years agoHelpfull: Yes(1) No(6)
• khooooob bada.........
• 7 years agoHelpfull: Yes(1) No(0)
• select 1 digit out of 9 = 9C1
  select 2 digit out of 9 = 9C2 arrange it in increasing order but arrangement doesn`t count here
  select 3 digit out of 9 = 9C3
  ---------------------------------------
  select 9 digit out of 9 = 9C9
  
  Total 9C1+ 9C2+9C3 ---- + 9C9= 2^9-1= 512-1= 511
  ANSWER 511
• 8 years agoHelpfull: Yes(0) No(3)
• Consider the string 123456789. Observe that each of the 9 digits in the string can safely be either included or not included, since failing to include a digit will not violate the increasing order of the digits. Hence, there are 2^9 possible strings that contain (0 or 1 or 2 or ... or 9) digits. However, we likely want to omit the case where there are 0 digits, which leaves us with a final answer of:
  2^9−1=511
• 8 years agoHelpfull: Yes(0) No(3)
• @naveen why u not include single digit in solution?
• 8 years agoHelpfull: Yes(0) No(1)
• why anyone doesn't considering single digit numbers ? and numbers like - 267 , or 389, 16789, 589 will not be accepted why ?? anybody explain
• 7 years agoHelpfull: Yes(0) No(0)
• The number is 123456789
  there are two possibility for each number (either they present or not)
  and there are 9 number having 2 possibility
  So, total combinations are : 2^9 =512
  but the string can't be empty,
  So, 512-1 = 511
  Ans: 511
• 7 years agoHelpfull: Yes(0) No(0)
• 1 digit with increasing and consecutive numbers : 9
  2 digit pairs with increasing and consecutive numbers : 8
  3 digit pairs with increasing and consecutive numbers : 7
  4 digit pairs with increasing and consecutive numbers : 6
  5 digit pairs with increasing and consecutive numbers : 5
  6 digit pairs with increasing and consecutive numbers : 4
  7 digit pairs with increasing and consecutive numbers : 3
  8 digit pairs with increasing and consecutive numbers : 2
  9 digit pairs with increasing and consecutive numbers : 1
  which is equal to 36+9=45.
• 7 years agoHelpfull: Yes(0) No(1)