How many ways A boy can reach the top of stairs which contain 10 steps, when he can take either one or two steps every time?

• Ans. 89
  
  case 1:1 1 1 1 1 1 1 1 1 1 > 1!
  case 2:1 1 1 1 1 1 1 1 2 > 9!/8!
  case 3:1 1 1 1 1 1 2 2 > 8!/6!*2!
  case 4:1 1 1 1 2 2 2 > 7!/4!*3!
  case 5:1 1 2 2 2 2 > 6!/4!*2!
  case 6:2 2 2 2 2 > 1!
  
  add answers of all cases => 1+9+28+35+15+1= 89
• 9 years agoHelpfull: Yes(53) No(1)
• 89....fibonacci series.. 1 2 3 5 8 13 21 34 65 89
• 9 years agoHelpfull: Yes(26) No(2)
• There will be 5 cases→
  1111111111,111111112,11111122,1111222,112222,22222
  Ans will be 89
  
• 9 years agoHelpfull: Yes(11) No(2)
• 55
  
  10c1+10c2=55
• 9 years agoHelpfull: Yes(9) No(8)
• See,
  No of ways to climb stair of 1 step - 1
  No of ways to climb stair of 2 step - "11 or 2" - 2
  No of ways to climb stair of 3 step - "111, 12, 21" - 3
  No of ways to climb stair of 4 step - "1111, 112, 121, 211, 22" - 5
  So clearly we can see a fibonacci series forming (which is sum of last two terms )
  
  No of ways to climb stair of 5 step - 5(steps for 4 step) + 3(steps for 3 step) = 8
  No of ways to climb stair of 6 step - 8(steps for 5 step) + 5(steps for 4 step) = 13
  Hence,
  No of ways to climb stair of 10 stp - 89
• 9 years agoHelpfull: Yes(7) No(0)
• using fibonacci series 1 2 3 5 8 13 21 34 65 89
• 9 years agoHelpfull: Yes(4) No(0)
• 89 is crrect ans
  
• 9 years agoHelpfull: Yes(3) No(1)
• the solution has to follow fibonacci series in the order of 1,2,3,5,8...till the 10th term and the solution emerges as 89 indeed. its not the case of combination or permutation. if there are n steps we have F(n) ways to climb the top and for this case n=10 where F denotes fibonacci series
• 9 years agoHelpfull: Yes(3) No(1)
• 10c1+10c=55.
  
• 9 years agoHelpfull: Yes(1) No(3)
• 354224848179261915075
  
  100th fibonacci number
• 9 years agoHelpfull: Yes(1) No(4)
• 2^10
  at every step he will have two options thus 2^10
• 9 years agoHelpfull: Yes(1) No(1)
• The boy can select either one step or two steps.
  If he chooses 1 step at a time he need 10 steps which is intuitive or by 10C1 = 10
  If he chooses 2 steps at a time he has 10C2 ways i.e., 45
  so 10 + 45 = 55
  Remember when "or" is mentioned in the problem then you need to add the ways and multiply when "and" is mentioned in the problem
• 9 years agoHelpfull: Yes(1) No(3)
• last digit=6 ,last power=4........(6)^4=1296
  last digit =96
• 9 years agoHelpfull: Yes(0) No(3)
• 10c1+10c2
  10+45=55
• 9 years agoHelpfull: Yes(0) No(2)
• 89 is correct ans
  1 2 3 5 8 13 21 34 65 89
• 9 years agoHelpfull: Yes(0) No(2)
• 55
  10c1+10c2= 55
• 9 years agoHelpfull: Yes(0) No(2)
• here fibonacci series will be formed like 1step in 1 way 2nd in 2 ways 3rd in 3 4th in 5 5th in 8 like the sum of all will come 89 so ans = 89
• 9 years agoHelpfull: Yes(0) No(0)
• if select one by one =1
  if select 2 chnce is 9in 10 so 9=89
• 9 years agoHelpfull: Yes(0) No(0)
• 1step 2steps
  10 0=10=10!/10!=1
  8 1=9=9!/8!=9
  6 2=8=8!/6!*2!=28
  4 3=7=7!/4!*3!=35
  2 4=6=6!/2!*4!=15
  0 5=5=5!/5!=1
  1+9+28+35+15+1=89
• 9 years agoHelpfull: Yes(0) No(0)