# Lesson 3D: Probability Using Counting Methods

 Over the years, people have enjoyed the diversion and competition of board games. Even ancient societies have been known to play various sorts of board games. Mancala may well be the oldest board game in the world. Some of the earliest evidence is found in archaeological digs sponsored by National Geographic that searched back to 5000 BCE. Excavations of an ancient house uncovered a limestone slab with two parallel rows of circular depressions. The layout was easily recognizable to an archaeologist on the dig as a Mancala playing board, such as shown in this photograph. Mancalas popularity stems, in part, from the fact that it can be played with whatever medium happens to be around. For instance, in Africa, people often play with pebbles using hollows scooped into the earth, with seashells in rings in the sand, or with seeds and a specially carved wooden board.

Although the game has its origins in the African and Arab world, the game might have evolved in Egypt from boards and counters that were used for accounting and stocktaking. It is a completely mathematical game; its more complex versions have as much scope as chess, despite its primitive beginnings.

Today, Mancala is known by numerous names around the world. These names are taken from the local culture, using words that reflect where the game is played, the manner of winning, the method of play, and the board or counters used. In English, it is often referred to as Count and Capture .

Do you seem to have more success at board games than others have? Success is not a matter of luck; it depends on skills gained through experience in playing the game, skills such as strategy, and an intuitive appreciation of probability.

In this Training Camp , you will enhance your ability to determine probabilities. You will solve probability problems by using your knowledge of the Fundamental Counting Principle, permutations, and combinations developed in Unit 2.

By the end of this lesson, you should be able to

 solve a problem that involves probability and permutations solve a problem that involves probability and combinations