Latest TCS Aptitude Question SOLUTION: How many ways A boy can reach the top of stairs which contain 10 steps, when he can take either one or two steps every time?

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How many ways A boy can reach the top of stairs which contain 10 steps, when he can take either one or two steps every time?

Asked In TCS purva (9 years ago)

Solved ashwin rathore Read Solution (19)

Is this Puzzle helpful?   (18)   (5) Submit Your Solution Permutation and Combination

Read Solution (19) :

ashwin rathore  (9 years ago) Best Solution

Ans. 89

case 1:1 1 1 1 1 1 1 1 1 1 > 1!
case 2:1 1 1 1 1 1 1 1 2 > 9!/8!
case 3:1 1 1 1 1 1 2 2 > 8!/6!*2!
case 4:1 1 1 1 2 2 2 > 7!/4!*3!
case 5:1 1 2 2 2 2 > 6!/4!*2!
case 6:2 2 2 2 2 > 1!

add answers of all cases => 1+9+28+35+15+1= 89

Is this solution Helpfull? Yes (53) | No (1)  

mohit  (9 years ago)

89....fibonacci series.. 1 2 3 5 8 13 21 34 65 89

Is this solution Helpfull? Yes (26) | No (2)  

pranjul chandel  (9 years ago)

There will be 5 cases→
1111111111,111111112,11111122,1111222,112222,22222
Ans will be 89

Is this solution Helpfull? Yes (11) | No (2)  

pranav lohkare  (9 years ago)

55

10c1+10c2=55

Is this solution Helpfull? Yes (9) | No (8)  

Shivam  (9 years ago)

See,
No of ways to climb stair of 1 step - 1
No of ways to climb stair of 2 step - "11 or 2" - 2
No of ways to climb stair of 3 step - "111, 12, 21" - 3
No of ways to climb stair of 4 step - "1111, 112, 121, 211, 22" - 5
So clearly we can see a fibonacci series forming (which is sum of last two terms )

No of ways to climb stair of 5 step - 5(steps for 4 step) + 3(steps for 3 step) = 8
No of ways to climb stair of 6 step - 8(steps for 5 step) + 5(steps for 4 step) = 13
Hence,
No of ways to climb stair of 10 stp - 89

Is this solution Helpfull? Yes (7) | No   

G.K.S.PRASAD  (9 years ago)

using fibonacci series 1 2 3 5 8 13 21 34 65 89

Is this solution Helpfull? Yes (4) | No   

bhagwandas kushwaha  (9 years ago)

89 is crrect ans

Is this solution Helpfull? Yes (3) | No (1)  

Pragna Paramita Pal  (9 years ago)

the solution has to follow fibonacci series in the order of 1,2,3,5,8...till the 10th term and the solution emerges as 89 indeed. its not the case of combination or permutation. if there are n steps we have F(n) ways to climb the top and for this case n=10 where F denotes fibonacci series

Is this solution Helpfull? Yes (3) | No (1)  

Harshwardhan Rathore  (9 years ago)

10c1+10c=55.

Is this solution Helpfull? Yes (1) | No (3)  

Sarabeshwar  (9 years ago)

354224848179261915075

100th fibonacci number

Is this solution Helpfull? Yes (1) | No (4)  

Basil Sufyan  (9 years ago)

2^10
at every step he will have two options thus 2^10

Is this solution Helpfull? Yes (1) | No (1)  

Kailash Patil  (9 years ago)

The boy can select either one step or two steps.
If he chooses 1 step at a time he need 10 steps which is intuitive or by 10C1 = 10
If he chooses 2 steps at a time he has 10C2 ways i.e., 45
so 10 + 45 = 55
Remember when "or" is mentioned in the problem then you need to add the ways and multiply when "and" is mentioned in the problem

Is this solution Helpfull? Yes (1) | No (3)  

rimsha naaz  (9 years ago)

last digit=6 ,last power=4........(6)^4=1296
last digit =96

Is this solution Helpfull? Yes | No (3)  

Shubhanjali Khare  (9 years ago)

10c1+10c2
10+45=55

Is this solution Helpfull? Yes | No (2)  

Rajneesh Gupta  (9 years ago)

89 is correct ans
1 2 3 5 8 13 21 34 65 89

Is this solution Helpfull? Yes | No (2)  

vivek kumar  (9 years ago)

55
10c1+10c2= 55

Is this solution Helpfull? Yes | No (2)  

aditi ojha  (9 years ago)

here fibonacci series will be formed like 1step in 1 way 2nd in 2 ways 3rd in 3 4th in 5 5th in 8 like the sum of all will come 89 so ans = 89

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banupriya  (9 years ago)

if select one by one =1
if select 2 chnce is 9in 10 so 9=89

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radha  (9 years ago)

1step 2steps
10 0=10=10!/10!=1
8 1=9=9!/8!=9
6 2=8=8!/6!*2!=28
4 3=7=7!/4!*3!=35
2 4=6=6!/2!*4!=15
0 5=5=5!/5!=1
1+9+28+35+15+1=89

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