In a staircase, there ar 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 staricase?

• possibilities are
  
  case 1:
  2 steps =5
  1 steps=0
  
  to no of arrangements=1
  
  2 steps =4
  1 steps=2
  
  to no of arrangements= (6!)/2!*4!
  
  2 steps =3
  1 steps=4
  
  to no of arrangements=7!/(3!*4!)
  
  2 steps =2
  1 steps=6
  
  to no of arrangements=8!/(2!*6!)
  
  2 steps =1
  1 steps=8
  
  to no of arrangements=9!/(8!)
  
  2 steps =0
  1 steps=10
  
  to no of arrangements=1
  
  
  total arrangements =89 (add all)
  
  
  
• 11 years agoHelpfull: Yes(60) No(0)
• the child can climb from 1st step to 2nd step in 1 way.
  frm 1st step to 3rd step in 2 ways.
  frm 1st step to 3rd step in 3 ways.
  frm 1st step to 4th step in 5 ways.
  thus it forms fibonacci series 1,2,3,5,8,13,21,34,55,89.
  therefore she can climb 10 steps in 89 ways.
• 11 years agoHelpfull: Yes(13) No(0)
• possibilities are:
  
  2 steps 1 step number of arrangements
  5 0 1
  4 2 6!/(4!*2!)
  3 4 7!/(3!*4!)
  2 6 8!/(2!*6!)
  1 8 9!/(8!)
  0 10 1
  total= 89
• 11 years agoHelpfull: Yes(1) No(0)
• it is
  1 1 1 1 1 1 1 1 1 1 =10!/10!
  1 1 1 1 1 1 1 1 2 =9!/8 !
  1 1 1 1 1 1 2 2 = 8!/6!*2!
  1 1 1 2 2 2 =7!/3!*3!
  1 1 2 2 2 2 =6!/2!*4!
  2 2 2 2 2 =5!/5!
  adding we get 89
• 8 years agoHelpfull: Yes(1) No(0)
• short cut: Fibonacci series 1 2 3 5 8 13 21 34 55 89
• 8 years agoHelpfull: Yes(0) No(0)