Counting and Probability

Learn all about Counting and Probability!

Counting

There are 4 branches in counting which are:

-Factorial Notation: We use factorial notation for a simple way of writing the product of all the positive whole numbers up to a given number.

-Basic Principles of Counting (Addition and Multiplication Rules): We use these basic principles to develop a few counting techniques. Such techniques will enable us to count the following, without having to list all of the items.

-Permutations: An arrangement (or ordering) of a set of objects is called a permutation. (We can also arrange just part of the set of objects.) The order that we arrange the objects is important.

-Combinations (Unoredered Selections): A combination of n objects taken r at a time is a selection which does not take into account the arrangement of the objects. That is, the order is not important.

Probablity

To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring.

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Basic Probability and Simple Experiments (ex.1)

Example

FACTORIAL NOTATION: n factorial is defined as the product of all the integers from 1 to n (the order of multiplying does not matter) .

We write "n factorial" with an exclamation mark as follows: n!

n! = (n)(n − 1)(n − 2)...(3)(2)(1)

5! = 5 × 4 × 3 × 2 × 1 = 120