College Math

College Math Study Guide

Let use learn some simple rules of counting that helps to solve such problems. Before moving to the rules, let us solve one simple problem of counting. Suppose Emily, who resides in city A, wishes to go to city C via city B. It is known that there are three different routes between city A and B, and then there are two different routes between city B and C. Now we have to calculate how many options does Emily have? Let us understand this by drawing a tree diagram . Tree diagram refers to the graphical representation of all possible outcomes.

In the above case, Emily has a total of six options to travel from city A and City C via city B, that are ad, ae, bf, bg, ch, and ci . Hence, there are a total of six options. It will be tough to count the total possibilities if the sample space is much higher. Sample space refers to the set of all possible outcomes. 4.2 Fundamental Counting Principle If one event occurs in m ways, and another event occurs in n ways after the occurrence of m, then the total number of ways in which the two events can occur is calculated as m X n ways. In the above example, Emily can travel between city A and city B in three possible ways, and the number of ways in which between city B and C is two. Applying the fundamental counting principle, the total numbers of ways in which Emily can travel are 3 * 2 = 6 ways. Let us take a few more examples to gain expertise in the concept. Remember the Cocoberry Frozen Yogurt offering the choice of 6 base flavors of yogurt and 12 options of toppings? We can calculate the total number of possibilities of different yogurts from the store using the counting principle. In this case, m = 6 and n = 12. Thus, we can say that there are 6*12 = 72 ways of selecting the frozen yogurt at Cocoberry . Now, let us consider an example with a bigger sample space. In a country, the automobiles bear license plates with a combination of different letters and digits, such that the initial 2 positions are

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