The correct order of sentences that logically fits together is:

**B. c - a - f - b - d - e**

Explanation of the correct sequence:

- **c. Firstly, You can live a long, healthy life and get in shape by playing sports. To improve your health and level of activity, take up a sport.**  
  This introduces the benefits of playing sports, so it comes first.

- **a. Also, Serious illnesses, like heart attacks and high blood pressure, may be less likely to strike you.**  
  This continues the idea that playing sports has health benefits.

- **f. Looking at the bright side of sports, there are a lot of advantages.**  
  This serves as a transition, summarizing the positive aspects of sports.

- **b. In addition to this, it increases your resistance to illness. In leisure time, you can play sports with your friends or your relatives, this not only helps you but also motivates everyone around you to take part in sports and have good health.**  
  This builds on the idea of health benefits and the social aspect of playing sports.

- **d. Last but not least, Sports also demonstrate an individual's level of activity and creativity while teaching them how to communicate with their teammates.**  
  This introduces other positive aspects of sports, such as creativity and teamwork.

- **e. Looking at the bright side of sports, there are a lot of advantages.**  
  This wraps up the passage by reiterating the many benefits of playing sports.

This sequence forms a cohesive and logically flowing paragraph about the advantages of playing sports.