Latest TCS Aptitude Question SOLUTION: 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 ch

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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

Asked In TCS Hari Priya Kazipeta (11 years ago)

Unsolved Read Solution (11)

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Read Solution (11) :

Sheik Shoyeb  (11 years ago)

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//

Is this solution Helpfull? Yes (66) | No (4)  

Khairul  (11 years ago)

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

Is this solution Helpfull? Yes (45) | No   

Khairul  (11 years ago)

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

Is this solution Helpfull? Yes (11) | No   

abhishek upadhyay  (11 years ago)

ansewr should be A. none oh the choice.

Is this solution Helpfull? Yes (7) | No (14)  

Sheik Shoyeb  (11 years ago)

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..

Is this solution Helpfull? Yes (6) | No   

shlesha91  (11 years ago)

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.

Is this solution Helpfull? Yes (3) | No   

vijai  (11 years ago)

ans . none
but i think correct ans for this ques s 231....
hint:1+2+3+5+8+13+21+34+55+89=231

Is this solution Helpfull? Yes (2) | No (13)  

satyanarayana  (11 years ago)

plx give detail xplanation i am unable to understand plz.

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Arun Sairam  (11 years ago)

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

Is this solution Helpfull? Yes (2) | No (12)  

teja  (11 years ago)

89 is the ans

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venkatesh  (11 years ago)

hari priya plz send de tcs papers to dimpu.k@gmail.com ...
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

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