Question

ou are climbing a stair case. it takes n steps to reach to the top. each time you can either climb 1 or 2 steps. in how many distinct ways can you climb to the top?

Answer 1

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