On a circumference of a given circle with a radius R two random points A & B are independently chosen.
What is the probability of AB being less than R ?
Design a schedule for a 10-week season involving 8 teams playing one game a week, on Sunday. The teams are divided into two divisions, east and west.
Each team plays the teams in its division twice, home and away.
Each team plays the teams in the other division once.
Each team plays 5 home games and 5 away games.
No team ever has 3 home games in a row, or 3 away games in a row