In a staircase, there are 10 steps. A child is attempting to climb the staircase. Each time, she can either make 1 step or 2 steps. In how many different ways can she climb the stair case?
a. 10 b. 21 c. 36 d. None of these.

• 
  she can go by
  1 steps-1 way
  
  that is choosing 1 two-step in 9 moves:
  9C1 : 9 ways//
  
  2 two-steps:
  choosing 2 two-steps in 8 moves:
  8C2 = 28 ways//
  
  3 two-steps
  7C3 = 35 ways//
  
  4 two-steps//
  6C4 = 15 ways//
  
  5 two-steps//
  which covers all the 10 stairs.. that means only one way
  2 2 2 2 2 = 1 way//
  
  Adding all the ways:
  1 + 9 + 28 + 35 + 15 + 1 = 89 ways//
• 11 years agoHelpfull: Yes(110) No(8)
• He can go by 1 step or 2 step
  So a recurrence relation can be formed as
  
  T(n) = T(n-1) + T(n-2) ;
  
  T(n) is the no of ways for climbing 'n' steps
  T(n-1) is the no of ways for climbing 'n-1' steps
  T(n-2) is the no of ways for climbing 'n-2' steps
  
  T(1) = 1 and T(2) = 2
  
  T(3) = T(2) + T(1) = 2 + 1 = 3
  
  T(4) = T(3) + T(2) = 3 + 2 = 5
  
  T(5) = T(4) + T(3) = 5 + 3 = 8
  
  T(6) = T(5) + T(4) = 8 + 5 = 13
  
  T(7) = T(6) + T(5) = 13 + 8 = 21
  
  T(8) = T(7) + T(6) = 21 + 13 = 34
  
  T(9) = T(8) + T(7) = 34 + 21 = 55
  
  T(10) = T(9) + T(8) = 55 + 34 = 89 ways//
  
• 9 years agoHelpfull: Yes(33) No(4)
• Using only 1-steps: 1 way
  Using only 2-steps: 1 way
  Using two 1-steps & four 2-steps: 6!/4!2!=15 ways
  Using four 1-steps & three 2-steps: 7!/4!3!=35 ways
  Using six 1-steps & two 2-steps: 8!/6!2!=28 ways
  Using eight 1-steps & one 2-steps: 9!/8!1!=9 ways
  TOTAL : 89 ways
  
• 9 years agoHelpfull: Yes(26) No(1)
• fibonaaci series logic is very best to solve this problem.
  answer is 89
• 8 years agoHelpfull: Yes(12) No(0)
• ans d none of these
• 11 years agoHelpfull: Yes(11) No(11)
• ans will be 10
  
• 11 years agoHelpfull: Yes(4) No(31)
• there are 10 steps right so by 1 step climbin all she can go in 1 way.
  if she goes by takin one two step and remainin 8 steps by 1 step each..den she can go in 9c1 ways..i.e only 1 two step next 8 one step climbin.
  by takin 2 two steps remainin 6 steps can be climbed in 8c2 ways..and so on like tat..3 two steps. :SUKRATI PANDEY
• 11 years agoHelpfull: Yes(3) No(4)
• ans is not clear enough to understand
  
• 9 years agoHelpfull: Yes(2) No(4)
• answer is d
  explanation:
  For 1st step there is one way
  1-1 way
  2-2 ways
  3-3 ways
  4-5 ways
  so we can se the ways are in Fibonacci series so the next sequence is,
  5-8 ways
  6-13 ways
  7-21 ways
  8-34 ways
  9-55 ways
  10-89 ways
  so the total ways are 89 ways
  
  3-4 ways
  
• 8 years agoHelpfull: Yes(2) No(6)
• explain properly
• 11 years agoHelpfull: Yes(1) No(5)
• jaya prakash : i got d answer bt plz explain clearly
• 11 years agoHelpfull: Yes(1) No(9)
• for climbing the stair he have 2 option(either one step or two step).
  for each step he climbs he will be having 2 opions only to proceed further.
  but when he comes on 9th step of the stair he will have only one choice that is only 1 step.and on 10th step of stair case no choice(0)
  so total ways will be 2^8+1+0 ways.
• 11 years agoHelpfull: Yes(1) No(6)
• use fibonacci series -> 1 2 (starting two terms) next terms as 3 5 8 13 21 34 55 89....10 th is 89 so 89 ways
• 6 years agoHelpfull: Yes(1) No(0)
• 10 one-step in 10 moves: 10C10 ways = 1 way
  1 two-step and 8 one-steps in (1+8)=9 moves: 9C1 ways = 9 ways
  2 two-steps and 6 one-steps in (2+6)=8 moves: 8C2 ways = 28 ways
  3 two-steps and 4 one-steps in (3+4)=7 moves: 7C3 ways = 35 ways
  4 two-steps and 2 one-steps in (4+2)=6 moves: 6C4 ways = 15 ways
  5 two-steps 5 moves: 5C4 ways = 1 way
  
  Total number of different ways = 1+9+28+35+15+1=89
• 4 years agoHelpfull: Yes(1) No(0)
• 10C2+10C1/10C10 =46 (d)
• 11 years agoHelpfull: Yes(0) No(17)
• d. none of these because if she climbs 2 steps at a time she will only take 5 times to make it
• 3 years agoHelpfull: Yes(0) No(0)
• D. because the answer will be 89 ways of doing the thing
• 3 years agoHelpfull: Yes(0) No(0)