Solve and explain the math problem

[filip_go]

A person stands on an imaginary circle with a radius R facing the center of the circle O. The person can make a step to the left or to the right and then again step on the circle. The average length of their step is d. A series of n steps will be called a period. The statement is that the person dances if the final position of one period is at least one step to the right in accordance to the starting position.
1. How many possible dances can be performed during a given n?
2. Find the number of possible dances in which the person passes the circle for a given n during the most K periods.
3. Find the dominant element in the equation provided for the number of possible dances from point 2.
4. Using Sterling’s formula (given below), approximate the dominant element in the 3rd point.

[Guest]

Here's a more specific explanation for the dance the person performs:

If the person passes the starting position going from the right to the left (clockwise) before they stop, they have to pass the starting position going from the left to the right or in general, if the person passes the starting position X times going from the right to the left before they stop, they have to pass the starting position X times going from the left to the right.

[filip_go]

Here's a more specific explanation for the dance the person performs:
If the person passes the starting position going from the right to the left (clockwise) before they stop, they have to pass the starting position going from the left to the right or in general, if the person passes the starting position X times going from the right to the left before they stop, they have to pass the starting position X times going from the left to the right.

[Guest]

i would like to know how you would solve this problem