MATHEMATICS 10 QUARTER 3 REVIEWER, Study notes of Mathematics

Download MATHEMATICS 10 QUARTER 3 REVIEWER and more Study notes Mathematics in PDF only on Docsity! MATHEMATICS REVIEWER (3RD QUARTER) LESSON: PERMUTATION Permutation - Each possible arrangement. - The order or arrangement is important Formulas:  If n ≥ r then use P (n,r) = n ! (n−r )!  If n = r or if there is no r, then use P (n,n) = n! Fundamental Counting Principle - States that of activity A can be done in n, ways, act. B can be done in n2 ways, act C can be done simultaneously in n1∙n2∙n3 ways. Distinct or Distinguishable Permutation - Permutations (or arrangements) that can be distinguished from one another. Formula:  P = n! p ! q !r !… Circular Permutation - The total number of ways in which n distinct objects can be arranged around a fix circle. Formulas:  If permutation of a circular table, then use P = (n-1)!  If there are people that want to sit beside each other in a circular table, then use P = (n-r)! ∙r!  If there are people that don’t want to sit beside each other in a circular table, then use P = P1 – P2 n-factorial - The product of the positive integer n and all the positive integers less than n. n! = n(n-1) (n-2)…(3)(2)(1) Factorial Notation - If n is a positive integer, n factorial denoted by n! is a product of all positive integers less than or equal to n. n! = (n-1) (n-2)… (3)(2)(1) LESSON: COMBINATION Combination - It is selection or by choice. - Order or arrangement is not important. Event - A set of outcome of an experiment to which a probability is assigned. Experiment - Trial, any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. Outcome - A possible result of an experiment or trial, each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive. Probability - A number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1 or using the percentage notation in the range from 0% to 100% Chance - The possibility of something happening when chance is defined, it is called probability. Sample Space - Set of all possible outcomes or results of that experiment. Simple Event - One that can only happen in one way; has a single outcome Compound Event - More complex than a simple event, as it involves the probability of more than one outcome. - Events that consists of more than one outcome P (E) = number of ways the event canoccur number of possible outcomes Complement of an Event