Combinations and Permutations: Understanding r-Permutations and r-Combinations - Prof. Tod, Assignments of Discrete Structures and Graph Theory

Download Combinations and Permutations: Understanding r-Permutations and r-Combinations - Prof. Tod and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity! Lecture 14: Combinations and Permutations • Associated reading: Rosen, Section 4.3 • Homework: Section 4.3, problems 1,3,5,6,9,11,15,17,23,31,35,36 r-Permutations: The number of ways to order r objects from a set of n objects is P (n, r) = n(n− 1) · · · (n− r + 1). If r = n (in other words, all n objects are ordered) then this n permutation is called a permutation for short. Example 1. Suppose 3 people get on an elevator in a six-story building and each one gets off on a different floor. How many ways can this be done? 1 Example 2. How many injective functions are there from a set of 4 elements to a set of 6 elements? In general, how many injective functions are there from a set of m elements to a set of n elements? r-Combinations: The number of ways to choose r objects from a set of n objects is C(n, r) = n(n− 1) · · · (n− r + 1) r! = n! (n− r)!r! . A more common way of writing C(n, r) is ( n r ) 2