Combinatorics problem, show all work.
a. A flag is to be designed with 10 stripes. The strips can be red, yellow, or blue. No stripe should be the same color as the one below it. How many ways are there to color the flag?
b. How many sets of 3 different numbers each can be formed from the numbers {1, 2, 3, ..., 19, 20} if no 2 consecutive numbers are to be in a set?
Combinatorics problem, show all work. a. A flag is to be designed with 10 stripes. The...
Combinatorics easter problem, show all your work. a. I have one dozen eggs to color for Easter. I can color each one red, yellow, blue, green, or orange. How many ways are there to do this? b. I colored the eggs from part a. I now have 5 red eggs, 3 blue eggs, 1 green egg, and 3 orange eggs. (I did not color any yellow) Aside from their color, they are identical. I have 12 different hiding spots, each...
Combinatorics problem, show all work. a. There are 25 varieties of cereal and I'm going to pick six different kinds to bring home to the family. How many ways can I do that? b. Forty students compete in an essay contest. There will be a blue ribbon, a red ribbon, and a yellow ribbon (for first, second, and third place) and four "honorable mentions" that get white ribbons. How many ways are there to award prizes to the students.
9) How many different 6-color code stripes can be made on a van if each code consists of the colors green, red, blue, yellow, gold, and white? All colors are used only once.
A combinatorics problem to get a classroom ready. Show all your work. a. I have 60 students and I'm going to give each one a single gumdrop. One is all you need. There are 6 flavors. How many possible ways can the students get their sugary candy? b. I have 16 identical white teacups. I hate white teacups! I am going to paint them. I can paint each one Ivory, Cream, Eggshell, Lace, Bone, or Vanilla. How many ways are...
Combinatorics problem, show all work. 6. We are seating 13 people on one side of a rectangular table (like Da Vinci's painting of the Last Supper.) a. How many ways can we seat them? b. How many ways can we do it if Doug refuses to sit next to Gordon? c. How many ways can we do it if Doug insists on sitting to the right of Gordon (not necessarily next to him)*? *For this part, I may sit next...
The ordered list 1,2,3,4,5,6,7,8 each number is painted with one of the colors blue (B), Purple (P), Yellow (Y) and Grey (G). How many different ways can they be colored if two consecutive numbers can't have the same color? (Its possible for one of the colors to not be used). Explain the calculations.
Combinatorics Chessboard (8x8 grid), show all work. a. How many ways are there to put 8 (identical) pennies on a chessboard, so no two share a row, and no two share a column? b. How many ways are there to put 5 pennies on a chessboard, with the same restriction? c. How many ways are there to put 3 pennies and 5 nickles on the board, with the same restriction - no two coins share a row, no two coins...
Kelly has different books to arrange on a shelf; 2 blue, 4 green, and 3 red. Answer parts a through e below. (a) In how many ways can the books be arranged on a shelf? way(s) (Type a whole number.) (b) If books of the same color are to be grouped together, how many arrangements are possible? way(s) (Type a whole number.) (c) In how many distinguishable ways can the books be arranged if books of the same color are...
math proof - 1 Problem I. (a) Let R be an 82 × 4 rectangular matrix each of whose entries are colored red, white or blue. Explain why at least two of the 82 rows in R must have identical color patterns (b) Conclude that R contains four points with the same color that form the corners of a rectangle. (c) Now show that the conclusion from part (b) holds even when R has only 19 rows. Hint: How many...
B ahorce Maca r e are 10 gerent sontware packages from which to select. How many different groups of software packages can be selected? 41 3. (14 points) A special deck of cards is formed by including a color and shape on each card, with numbers of cards available as shown in the table: Triangle Square Circle Total 20 12 Green 18 Red Total 136 Blue 61 One of these cards is randomly selected What is the probability that the...