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Mathematical route problem.
The first picture,

There are two steps down,

A There are two steps on the right.

So choose two of the four steps to the right, C 4 2 = 6.

Enumeration: lower right, lower right, lower right, lower right, lower right, lower right, lower right, lower right, lower right.

Second photo,

There are three steps down,

A There are four steps on the right.

A * * * is seven steps, choose three steps down, C 7 3=35.

There are too many such cases, so I won't list them one by one, but you can have a try.

The third picture,

There are five steps down,

A There are eight steps on the right.

A *** 13 step, select 5 steps down, C 13 5= 1287.

See the pattern?