PPT-Fundamental Counting Theory, Permutations and Combinations

DM 13 The Fundamental Counting Theory A method for counting outcomes of multistage processes If you want to perform a series of tasks and the first task can be done in a ways the second can be done in b ways the third can be done in c ways and so on then all the tasks can be done in a x b x cways . Mr. Mark Anthony Garcia, M.S.. Mathematics Department. De La Salle University . Experiment: Definition. An . experiment . is a process that generates a set of data. .. Example 1: . Experiment. Tossing of a coin. Definition of Combination. An . arrangement. . of objects in which the . order. . of selection . does NOT matter. .. . Ex: You have to visit three out of your four friends houses: Andrew (A), Betty (B), Carlos (C), Dave (D). What are the different ways to select the 3 houses to visit?. Generating Permutations. Many different algorithms have been developed to generate the n! permutations of this set.. We will describe one of these that is based on the . lexicographic . (or . dictionary. Section 6.3. Section Summary. Permutations. Combinations. Combinatorial Proofs. Permutations. Definition. : A . permutation. of a set of distinct objects is an ordered arrangement of these objects. An ordered arrangement of r elements of a set is called an . Urn models. We are given set of n objects in an urn (don’t ask why it’s called an “. urn. ” - probably due to some statistician years ago) .. We are going to pick (select) r objects from the urn in. Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. Objective. : . To find the counts of various combinations and permutations, as well as their corresponding probabilities. CHS Statistics. Warm-Up. Alfred . is trying to find an outfit to wear to take Beatrice on their first date to Burger King. How many different ways can he make an outfit out of this following clothes:. Section 6.. 2. The Pigeonhole Principle. If a flock of . 20. pigeons roosts in a set of . 19 . pigeonholes, one of the pigeonholes must have more than . 1. pigeon.. Pigeonhole Principle. : If . with Repetitions. ICS 6D. Sandy . Irani. Permutation Counting. How many ways to permute the letters in the word “BAD”?. BAD. BDA. ABD. ADB. DAB. DBA. Permutation Counting. How many ways to permute the letters in the word “ADD”?. Evaluate the following. (7-3)! . 6! . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. . = . . . = . . .  .  . . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. Generating Permutations. Many different algorithms have been developed to generate the n! permutations of this set.. We will describe one of these that is based on the . lexicographic . (or . dictionary. Evaluate the following. 6!. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. 6! = 6 x 5 x 4 x 3 x 2 x 1. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle. Objectives. Permutations. Combinations. Vocabulary. A . permutation. is an arrangement of items in a particular order..