There is a square ABCD whose length of one side of is 1.
First, the point P is in the position of A.
When I throw one coin and head comes out, the point P moves 1 and tail comes out, P moves 2 in the direction of an arrow on the side.
When I throw coin 5 times, the point P came to the position of A.
In this case, how many kinds of way of head and tail coming out are there?
<Example> When throwing twice and coming to the position of D, there are two kinds, (Head, Tail),(Tail, Head).
Answer
10 kinds
Solution
When coin is thrown 5 times, the shortest is 1 × 5 = 5 and the longest is 2 × 5 = 10.
As P comes to A when it moves 4, 8, 12 -----, it is found total number is 8.
(8 - 1 × 5) / (2 - 1) = 3 which is the number head comes out.
Then (5 × 4 × 3) / (3 × 2 × 1) = 10 kinds.
