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)???

• 9 digit no= only one (123456789)
  8 digit no=9c1=9
  7 digit no=9c2=36
  6 digit no=9c3=84
  5 digit no=9c4=126
  4 digit no=9c5=126
  3 digit no=9c6=84
  2 digit no=9c7=36
  total=1+9+36+84+126+126+84+36=502
• 10 years agoHelpfull: Yes(77) No(12)
• yaaar 5 log 5 sol...sala kaun sa sahi hai be.... dimag ka dahi ho gaya ..
• 10 years agoHelpfull: Yes(62) No(6)
• I am giving you all the correct solution.. At first u gotta understand the question.. Numbers where digits are in increasing order . But if u thoroughly follow d examples , u would see that 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 . .. As I explained the question properly , now m pretty sure , u urself would be able to solve d problem , 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
  .. Dont forget to follow me on facebook ..my facebook id-www.facebook.com/adi1nonly ..
• 9 years agoHelpfull: Yes(34) No(9)
• it should be 9c1+9c2......+9c9 = 2^n - 1 = 2^9 - 1 = 411. Since numbers can be chosen in these many ways and ascending order for any combination is only one.
• 12 years agoHelpfull: Yes(21) No(20)
• Ans: 502
  
  9 digit no- 1,2,3,4,5,6,7,8,9 can be formed in only 1 way= 9C0
  
  8 digit no can be formed by taking out one no. from the above series. This can be done in 9C1 ways as after eliminating any one no. from the series, it continues to remain in ascending order
  
  similarly, 7 digit no. can be formed in 9C2 ways
  
  6 digit in 9C3 ways
  
  5 digit in 9C4 ways
  
  ....
  ....
  
  3 digit no. in 9c7 ways
  
  therefore total: 9C0+9C1+9C2+9C3+9C4+9C5+9C6+9C7= 2^9-(9C8+9C9)= 502 ways
  
  
  
  
  
  
  
  
• 9 years agoHelpfull: Yes(20) No(4)
• 502 is correct answer. The question is given in Arun Sharma Quantitative aptitude in permutation and combination LOD III question no. 6
• 10 years agoHelpfull: Yes(15) No(6)
• Numbers starting with "1"are 2 digit(12,13,14,15,16,17,18,19) total of "8"
  3 digit(13,14,15...........19) total "7"
  similarly 4 digit total of "6" continuing....
  9 digits total of "1"
  Now numbers starting with "2" are 2 digits(23,24,25,26,27,28,29) total "7"
  3 digits(234,245,256,267,278,289)total of "6"
  similarly 4 digits total of "5" continuing....
  8 digits total of "1"
  continuing we get no's(including all digits except 1) in increasing order starting with
  1=(8+7+6+5+4+3+2+1)=8!
  2=(7+6+5+4+3+2+1)=7!
  3=(6+5+4+3+2+1)=6!
  4=(5+4+3+2+1)=5!
  5=(4+3+2+1)=4!
  6=(3+2+1)=3!
  7=2!
  8=1!
  now 1 digit nos possible are 1,2,3,4,5,6,7,8,9 a total of 9
  Answer=8!+7!+6!5!+4!+3!+2!+1! + 9 = 46242
• 12 years agoHelpfull: Yes(12) No(31)
• 9 digit no-(123456789)= 1
  8 digit no-(12345678, 23456789)=2
  7 digit no-(1234567, 2345678, 3456789)=3
  6 digit no-(123456, 234567, 345678,456789)=4
  5 digit no-(12345, 23456, 34567, 45678, 56789)=5
  4 digit no-(1234, 2345, 3456, 4567, 5678, 6789)=6
  3 digit no-(123, 234, 345, 456, 567, 678, 789)=7
  2 digit no-(12, 23, 34, 45, 56, 67, 78, 89)=8
  Hence, 1+2+3+4+5+6+7+8= 36(no will be in increasing order so any no like 23451,78912 will not be accepted).
  
• 8 years agoHelpfull: Yes(8) No(9)
• ans 255
  no. containing 9 is 9
  no. containing 8 is 8 89
  no. containing 7 is 7 78 79 789
  no. containing 6 is 6 67 68 69 678 689 679 6789
  .
  .
  .
  it form gp 1+2+4....2^8= (2^8-1)=255
  
• 10 years agoHelpfull: Yes(5) No(10)
• 12...9,12...8,12...7,12...6,12...5,12...4,12..3,12,23...9,23...8,23...7,23....6,23....5,23....4,23..... in same manner last 89...so from 1 as a starting digit total 8 no's,from 2 as a starting digit total 7 no's.so like that 8+7+6+5+4+3+2+1=36 ans
  
• 10 years agoHelpfull: Yes(5) No(6)
• sum of 8c1 to 8c8+ sum of 7c1 to 7c7+.....+2c1+2c2+1c1... gives answer
• 12 years agoHelpfull: Yes(4) No(15)
• 502 is the ryt ans...
  
• 8 years agoHelpfull: Yes(4) No(4)
• there will be 35 numbers eight numbers will be started from 1, seven number will be started from 2 and so on .
• 12 years agoHelpfull: Yes(3) No(9)
• one digit no is formed=9
  n toatal no is=502+9
  511
• 9 years agoHelpfull: Yes(3) No(2)
• 45
  no starting with 1 9 no
  2 8
  "
  "
  "
  9 is only 1
  
  total no is 45
• 8 years agoHelpfull: Yes(2) No(2)
• starting from 1=8+7+6+5+4+3+2+1
  from 2=7+6+5+4+3+2+1
  from 9=0;
  total=120
  
• 10 years agoHelpfull: Yes(1) No(5)
• if we consider only 1 digit then it should be done in 9 ways.
  if we consider 2 digits then it should be done in 8 ways, like {(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9)} in increasing order.
  if we consider 3 digits then it should be done in 7 ways, like {(1,2,3),(2,3,4),(3,4,5),(4,5,6),(5,6,7),(6,7,8),(7,8,9)} in increasing order.
  and so on by considering 4,5,6,7,8,9 digits in increasing order.
  Therefore the result is: 9+8+7+6+5+4+3+2+1=45
• 10 years agoHelpfull: Yes(1) No(4)
• ans.45
  1 digits=9
  2 digits=8
  .
  .
  .
  9 digits=1
  so sum =(1+2+3+4+5+6+7+8+9)=45
• 10 years agoHelpfull: Yes(1) No(4)
• 1 digit : 1,2,3,4,5,6,7,8,9 => 9 number
  2 digit no.: 12,23,34,45,56,67,78,89 => 8 number
  3 digit no: 123,234,345,456,567,678,789 +> 7 numbers
  4 digit no: 6
  5 digit no:5
  6 digit no: 4
  7 digit no: 3
  8 digit no: 2
  9 digit no: 1
  total numbers= 1+2+3+4+5+6+7+8+9 =45
• 9 years agoHelpfull: Yes(1) No(3)
• when we select 1 then we are getting only 1 digit....(2^1) -1
  when we are selecting 2 then taking into consideration that 1 is there the nos. can be.. 1, 2, 12 ie 3 digits then we can denote it by (2^2) -1
  again when we select 3 then taking into consideration that 1 and 2 are there , the numbers can be 1,2,3,12.13,23, 123 ie 7 numbers and we can denote it by (2^3)-1
  SO the form we are getting is [(2^d) -1]
  Putting d=9 we get 511(ANSWER)
  the other method is
  9c1+9c2+9c3....9c9=[2^9] -1= 511
  Formulae used is nc0 +nc1 +nc2........+ncn = 2^n
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• Its only a combination, how can u say that it will be arrange in assending order.
  Could u pls give me exact reason of the answer 502.
• 8 years agoHelpfull: Yes(1) No(1)
• correct solution is:
  9c1 +9 c2 +9 c3+9 c4+ 9 c5+ 9 c6+9 c7 + 9 c8+ 9 c9
• 7 years agoHelpfull: Yes(1) No(0)
• 2 digit no:- 8 {12,23,34,45,56,67,78,89}
  3 digit no:- 7
  4 digit no:- 6
  5 digit no:- 5
  6 digit no:- 4
  7 digit no:- 3
  8 digit no:- 2
  9 digit no:- 1
  Total sum= 8+7+6+5+4+3+2+1=36
• 7 years agoHelpfull: Yes(1) No(0)
• 2 digit 12,23,34,45,56,67,78,89 possible in increasing order 8
  3 digit 123,234,345,456,567,678,789........7
  
  4 digit 1234,2345,3456,4567,5678,6789........6
  
  5 digit similarly.......5
  6 digit...........4
  7 digit...........3
  8 digit............2
  9 digit.............1
  
  Total= 8+7+6+5+4+3+2+1=36
• 6 years agoHelpfull: Yes(1) No(0)
• arey yaar...just dont confuse with these many solutions....so vch among these is the right one?
  
• 10 years agoHelpfull: Yes(0) No(3)
• no with 9 digit possible is only 1 i.e 123456789--- 1
  now with 8 digit 1 at 1st place then at 2nd 3rd 4th ....8th each position has 2 choice that gives us total 14 + 1 when digit 2 at first den only 1 choice hence total 15.
  similarly when 7digit no framed 1 digit at 1st place den for other 6 position 3 choices each position 18 + when 2nd digit at 1st place choices 12 + 1 when 3rd at 1st place ..hence total 18+12+1=31
  similarly for 6 digit no 20+15+10+1=46
  5digit no 20+16+12+8+1=57
  4digit no 18+15+12+9+6+1=61
  3digit no 14+12+10+8+6+4+1=55
  2digit no 8+7+6+5+4+3+2+1=36
  total=36+55+61+57+46+31+15+1=302
• 10 years agoHelpfull: Yes(0) No(2)
• 1->9
  2->36
  3->84
  4->252
  5->252
  6->84
  7->36
  8->9
  9->1
  ...... ans iz 763
• 9 years agoHelpfull: Yes(0) No(1)
• as there r 9 digit.....so for every digits no...9fact.....8 fact.......7 fact...........................1 fact..add them...
  
• 9 years agoHelpfull: Yes(0) No(1)
• i think its 256... as the posibilities keeps doubling for every starting number.. viz.,the numbers starting with 9 is- 1 possiblity(1),the numbers starting with 8 is -2 possib(8,89),the numbers starting with 7 is-4 possib(7,78,79,789), starting wd 6 is -8(6,67,68,69,678,679,689,6789),the numbers starting with 5 is- 16(5,56,57,58,59,567,568,569,578,579,589,5678,5679,5689,5789,56789),the numbers starting with 4 is-32,the numbers starting with 3 is -64,the numbers starting with 2 is-128, so finally, the the numbers starting with 1 is -256. so i think its 256 numbers can be formed .. SO ANSWER IS 256
• 8 years agoHelpfull: Yes(0) No(1)
• Sorry guys there was a mistak ein my calculation.. procedure is correct..SO answer is 511... as the posibilities keeps doubling for every starting number.. viz.,the numbers starting with 9 is- 1 possiblity(1),the numbers starting with 8 is -2 possib(8,89),the numbers starting with 7 is-4 possib(7,78,79,789), starting wd 6 is -8(6,67,68,69,678,679,689,6789),the numbers starting with 5 is- 16(5,56,57,58,59,567,568,569,578,579,589,5678,5679,5689,5789,56789),the numbers starting with 4 is-32,the numbers starting with 3 is -64,the numbers starting with 2 is-128, so finally, the the numbers starting with 1 is -256. so i think its 511 numbers can be formed .. SO ANSWER IS 511 :-)
• 8 years agoHelpfull: Yes(0) No(4)
• if u thoroughly follow d examples , u would see that 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 . .. As I explained the question properly , now m pretty sure , u urself would be able to solve d problem , 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
• 7 years agoHelpfull: Yes(0) No(1)
• Left to Right in increasing order but consecutive increasing order should be must ..
  Digits are using -(1,2,3,4,5,6,7,8,9)
  Start from two digits- 12, 23, 34, 45, 56, 67, 78, 89----(8 total number of ways)
  Thee digits---123, 234, 345, 456, 567, 678, 789------(7 total number of ways)
  Four digits-- ------6 ways, Five digits ---- 5 ways , Six digits-- 4 ways,
  Seven digits---- 3 ways , Eight digits-- 2 ways , Nine digits --- 1 ways
  in above solution we can see a beauty of numbers
  Number of Digits--- Number of ways
  2--8, 3-7, 4--6, 5--5, 6--4, 7--3, 8--2, 9--1,
  so 8+7+6+5+4+3+2+1=36 ans
• 7 years agoHelpfull: Yes(0) No(1)
• Those who are saying 502 are not using there brain and just using the book formula.
  How can 8 digits number can be formed in 8 ways or 7 digits in 36 ways.........??? Use your brain before answering question.
  Already mentioned in question that the numbers should be in increasing order so solution is:
  
  9 digit no-(123456789)= 1
  8 digit no-(12345678, 23456789)=2
  7 digit no-(1234567, 2345678, 3456789)=3
  6 digit no-(123456, 234567, 345678,456789)=4
  5 digit no-(12345, 23456, 34567, 45678, 56789)=5
  4 digit no-(1234, 2345, 3456, 4567, 5678, 6789)=6
  3 digit no-(123, 234, 345, 456, 567, 678, 789)=7
  2 digit no-(12, 23, 34, 45, 56, 67, 78, 89)=8
  Hence, 1+2+3+4+5+6+7+8= 36
• 1 year agoHelpfull: Yes(0) No(0)