16. There is a staircase with 10 steps. A child runs up the steps, either 1 or 2 steps with each stride. How many different ways can the steps be climbed by her?

a. None of the choices
b. 45
c. 89
d. 10

• All possibilities:
  steps:
  _ _ _ _ _ _ _ _ _ _
  
  No 2 steps All 1's:
  
  1 1 1 1 1 1 1 1 1 1 => 1 way//
  
  1 two step:
  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//
  
  
  
  
• 12 years agoHelpfull: Yes(66) No(4)
• 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
  
  
• 12 years agoHelpfull: Yes(45) No(0)
• 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
  
  
• 12 years agoHelpfull: Yes(11) No(0)
• ansewr should be A. none oh the choice.
• 12 years agoHelpfull: Yes(7) No(14)
• MR. ARUN SAIRAM
  
  i can prove this from ur method also..
  
  from 9-10 its one way
  from 8-10 its 2 ways..
  from 7-10 its 3 ways..
  from 6-10 its 5 ways..
  .
  
  
  .
  from 2-10 its 34 ways
  from 1-10 its 55 ways
  from 0-10 its 89 ways
  
  then y are u adding them..
  its straight away.. from 0 to 10, he can go in 89 ways..
  
• 12 years agoHelpfull: Yes(6) No(0)
• n+2m=10
  possible solutions are
  0,10 gives 10!/10!*0! ways
  2,4 gives 6!/2!*4! ways
  4,3 gives 7!/4!*3! ways
  6,2 gives 8!/6!*2! ways
  8,1 gives 9!/8!*1! ways
  10,0 gives 10!/10!*0! ways
  total =89 ways.
• 12 years agoHelpfull: Yes(3) No(0)
• ans . none
  but i think correct ans for this ques s 231....
  hint:1+2+3+5+8+13+21+34+55+89=231
• 12 years agoHelpfull: Yes(2) No(13)
• plx give detail xplanation i am unable to understand plz.
  
• 12 years agoHelpfull: Yes(2) No(3)
• MR.SHIEK SHOYEB is wrong.... its none of these.
  from 9-10 there is 1 way
  from 8-10 there is 2 ways i.e 8-9 9-10 or 8-10
  from 7-10 there is 3 ways i.e 7-8 8-9 9-10,7-9 9-10,7-8 8-10
  similarly it continues in fibonacci series
  so add first ten fibonacci serite i.e 1+2+3+5+8+13+21+34+55=142 ways is the answer as explained by people from FACE academy whn they took training for us. so answer as viewing the options is a.none of these
  
• 12 years agoHelpfull: Yes(2) No(12)
• 89 is the ans
• 12 years agoHelpfull: Yes(0) No(0)
• hari priya plz send de tcs papers to dimpu.k@gmail.com ...
  plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
• 12 years agoHelpfull: Yes(0) No(0)