Latest TCS Aptitude Question SOLUTION: 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 stari

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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?

Asked In TCS vishal kumar singh (10 years ago)

Unsolved Read Solution (5)

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Read Solution (5) :

Ishan  (10 years ago)

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)

Is this solution Helpfull? Yes (60) | No   

tejaswi boni  (10 years ago)

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.

Is this solution Helpfull? Yes (13) | No   

Ishan  (10 years ago)

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

Is this solution Helpfull? Yes (1) | No   

swathi  (8 years ago)

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

Is this solution Helpfull? Yes (1) | No   

PATAN SABIHA  (7 years ago)

short cut: Fibonacci series 1 2 3 5 8 13 21 34 55 89

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