Discrete Math 2. For this problem, you may want to review set theory from CSE 20, especially the size of power set of a set. (6 points) Let n be a positive integer and define [nl to be the set of the first n positive integers That is, n] 1,2,3,... many ways can we do this? (Optional.) Now we want to select three subsets A, B, C of n such that AC C, B C C, and An B ....
For this problem, you may want to review set theory from CSE 20, especially the size of power set of a set. (6 points) Let n be a positive integer and define [n] to be the set of the first n positive integers. That is, [n] = {1, 2, 3, . . . , n}. We want to select two disjoint subsets A, B of [n]. In how many ways can we do this? (Optional.) Now we want to select...
1. A universal set, with n(U)70, is partitioned into three subsets: A, B, and C. If n(B) 3-n(A), and n(C) 2-n(B), find the number of elements in the subset A. 2. A license plate consists of eight symbols on each plate, where the first three symbols are letters of the alphabet and the following five symbols are the digits selected from the set f0, 1, 2, 3, 4, 5, 6, 7, 8, 9)? How many license plates can be produced...
Counting subsets 4. (a). How many ways are there to rearrange (all of) the letters of SPIDERMAN so that all of the consonants appear in alphabetical order (not necessarily consec- utively)? (b). How many ways are there to rearrange (all of) the letters of SPIDERMAN so that the word PRIDE appears together as a word somewhere? (c). How many ways are there to rearrange (all of) the letters of SPIDERMAN that begin and end with a vowel? (d). How many...
A carton of eggs contains two bad ones. In how many ways can we select three of the 12 eggs so that a) none of the bad ones are included, b) both of the bad ones are included; c) one of the bad ones are included?
5. Binomial Coefficients (a) How many subsets with at least 5 elements does a set with 8 elements have? n+3 (b). Find the coefficient of z" in (3-2)+ (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20? 5. Binomial Coefficients (a) How many subsets with at least 5 elements does a set with 8 elements have? n+3 (b). Find the coefficient of z" in (3-2)+ (c). How...
Suppose we want to choose 4 colors, without replacement, from 16 distinct colors. (a) How many ways can this be done, if the order of the choices does not matter? x 6 ? (b) How many ways can this be done, if the order of the choices matters?
Suppose we want to choose 7 objects, without replacement, from 11 distinct objects. (a) How many ways can this be done, if the order of the choices is not relevant? Х 5 ? E (b) How many ways can this be done, if the order of the choices is relevant? 0
Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair. (a) How many ways can this be done, if the order of the choices matters? х ? 0 (b) How many ways can this be done, if the order of the choices does not matter?
For the word CHARITY, a) How many ways can we arrange all letters? b) How many ways can we select three letters? c) How many ways can we arrange three letters? d) How many ways can we arrange all the letters such that it begins with ‘CHA’?