For each system in Exercise 2 that is linear, determine whether it is consistent

Math 3160 – Textbook Notes A First Course in Probability Chapter 1 – Combinatorial Analysis  Introduction o Many problems in probability theory can be solved simply by counting the number of different ways that a certain event can occur o Enumeration is basic laying out of arrangements o Mathematical theory of counting is known as Combinatorial Analysis  The Basic Principle of Counting o One experiment can result in m number of outcomes o One experiment can result in n number of outcomes o Together there are mn possible outcomes of the two experiments  Permutations o How many different ordered arrangement of the letters a, b, and c are possible o When there are n objects, the number of permutations or combinations is  n!  or n factorial  or n(n-1)(n-2)…(3)(2)(1) o If there are repetitions of objects, or non distinct objects  n! / r1!r2!  where r1 and r2 are the number of repetitions of objects 1 and 2  Combinations o Combinations are the number of different groups of r objects that could be formed from n objects o ( ) r  Self Test Problems: o 1. How many different linear arrangements are there of the letters A, B, C, D, E, F for which  a. A and B are next to each other  5!2! = 240  b. A i