Question

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?

Answer 1

1 2 2
221
212
these are the steps he can cross it

Answer 2

The number of ways in which the man can cross the river taking either 1 or 2 steps at a time is 13.

Answer:

There are 5 floating stones in river

A man can cross the river by either taking 1 or 2 steps at a time

To cross the river, the man must take six steps. He can accomplish this in several ways:

Crossing the river in 6 unit steps equals one way.

4 unit steps and 1 double step = 5C1 = 5C4 = 5 ways to cross the river.

2 unit steps and 2 double steps = 4C2 = 6 ways to cross the river.

3 double steps across the river = 1 way.

As a result, the required number of ways equals 1 + 5 + 6 + 1 = 13.

∴ The number of ways in which the man can cross the river taking either 1 or 2 steps at a time is 13.

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