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?
Answers
Number of ways if he goes by 'one step' = 1
Number of ways of choosing 1 'two step' in 9 moves = 9C1 = 9
Number of ways of choosing 2 'two steps in 8 moves = 8C2 = 28
Number of ways of choosing 3 'two steps' in 7 moves = 7C3 = 35
Number of ways of choosing 4 'two steps' in 6 moves = 6C4 = 15
Number of ways of choosing 5 'two steps' in 5 moves = 5C5 = 1
Total Number of ways = 1 + 9 + 28 + 35 + 15 + 1 = 89
Acc to the question, 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.
There are two methods for solving this question. Firstly, you can use the general permutaion and combination and secondly you can also use the fibo series but the starting two terms as 1, 2.
If you follow the question carefully, then the number of ways will nothing but a fibonacci series for n=10.
Fibo series: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233........
Thus, the 10th term of the series will be 89.