Answer to Question #136875 in Combinatorics | Number Theory for Joseph Se

Question

Answer in brief and concise sentences.

A. What is Combinatorics?
B. State the Multiplication Rule of Counting
C. State the Addition Rule of Counting
D. Describe the 2 approaches of defining probability.

Answer 1

A) Combinatorics is a branch of Mathematics that deals with problems of selection, arrangement, and operation within a finite or discrete system it's objective being how to count without counting

B)The Multiplication Rule of Counting states that, if there are $a$ ways of doing something and $b$ ways of doing another thing, then there are $a. b$ ways of performing both actions.

C) The Addition Rule of Counting states that if there $A$ ways of doing something and $B$ ways of doing another thing and we can not do both at the same time, then there are $A+B$ ways to choose one of the actions.

D) Approaches of defining Probability

i) Classical Approach. . .

If an experiment has $n$ simple outcomes, this method would assign a probability of $\frac{1} {n}$ to each outcome. Meaning, each outcome is assumed to have an equal probability of occurrence.

ii) Subjective Approach. . .

Under this approach,we define probability as the degree of belief that we hold in the occurrence of ane vent. Hence,judgment is used as the basis for assigning probabilities.