Counting and Probability
Learn all about Counting and Probability!
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.
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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