QA – Placement Quizzes | Permutation and Combination | Question 8

There are 5 floating stones on a river. A man wants to cross the river. He can move either 1 or 2 steps at a time. Find the number of ways in which he can cross the river? (Man can’t take double step from last stone).
(A) 11
(B) 12
(C) 13
(D) 14

Answer: (C)
Explanation: The man needs to take 6 steps to cross the river. He can do this in the following ways:

• Crossing the river by 6 unit steps = 1 way.
• Crossing the river by 4 unit steps and 1 double step = ⁵C₁ = 5C4 = 5 ways.
• Crossing the river by 2 unit steps and 2 double steps = ⁴C₂ = 6 ways.
• Crossing the river by 3 double steps = 1 way.

Hence, the required number of ways = 1 + 5 + 6 + 1 = 13.
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