in a stair case there are 10 steps. a child is attempting to climb staircase. each time she can either make a step or 2. in how many different ways she can climb the staircase

1-10
2-21
3-36

• the possibilities are....
  
  1 1 1 1 1 1 1 1 1 1(just one way)
  1 1 1 1 1 1 1 1 2(9C1=9 way)
  1 1 1 1 1 1 2 2(8C2=28 way)
  1 1 1 1 2 2 2 (7C3=35 way)
  1 1 2 2 2 2(6C4=15 way)
  2 2 2 2 2(1 way)
  so total way(1+9+28+35+15+1)=89 way
• 9 years agoHelpfull: Yes(39) No(6)
• 1 1 1 1 1 1 1 1 1 1(just one way)= 1
  1 1 1 1 1 1 1 1 2 --> 9!/8! = 9
  1 1 1 1 1 1 2 2 --> 8!/(6!.2!) = 28
  1 1 1 1 2 2 2 --> 7!/(4!.3!) = 35
  1 1 2 2 2 2 --> 6!/(2!.4!) = 15
  2 2 2 2 2 --> (just one way) = 1
  
  1+9+28+35+15+1 === 89
• 9 years agoHelpfull: Yes(9) No(0)
• at each step that child has two possibilities.. so including ground 10*2=20
  but at the last step there will be only one possibility.. so answer is 20+1=21
• 9 years agoHelpfull: Yes(8) No(7)
• for step
  9-10=1 way
  8-9-10=2 way
  7-8-9-10=3 way
  6-7-8-9-10=4 way and so on
  now for step 1-2-3-4-5-6-7-8-9-10=10 ways
  
  therefore,1+2+3+......+10=55 Ans
  
  
  
• 9 years agoHelpfull: Yes(2) No(6)