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Combinatorics
- You have 10 beads numbered 1-10 that you want to put on a necklace....
You have 10 beads numbered 1-10 that you want to put on a necklace. No two...
You have 10 beads numbered 1-10 that you want to put on a necklace. No two even numbered beads can be next to each other, and no two odd numbered beads can be next to each other. How many distinct ways can you put the beads on a necklace? With explanation please!!
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three...
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three beads where all beads have different colors. a) How many different necklaces with N beads can be made with N distinct colors? b) How many different necklaces can you string together if you have to use 5 beads and up to 2 colors? c) Now suppose we can only...
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arra...
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three beads where all beads have different colors. a) How many different necklaces with N beads can be made with N distinct colors? b) How many different necklaces can you string together if you have to use 5 beads and up to 2 colors? c) Now suppose we can only...
3. An urn contains five white balls numbered from 1 to 5, five red balls numbered...
3. An urn contains five white balls numbered from 1 to 5, five red balls numbered from 1 to 5 and five blue balls numbered from 1 to 5. For each of the following questions, please give your answer first in the form that reflects your counting process, and then simplify that to a number. You must include the recipes. No other explanation needed. (a) In how many ways can we choose 4 balls from the urn? (b) in how...
A combinatorics problem to get a classroom ready. Show all your work. a. I have 60...
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. a. A flag is to be designed with 10 stripes. The...
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?
please illustrate each stepbof the solution so I can understand thank you 4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if tw...
please illustrate each stepbof the solution so I can
understand
thank you
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if two colors (red and blue) are available? (b) How many ways, if additionally we want that at most two numbered vertices are painted red?
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint...
You have a pair of 4-sided dice. The four sides of each die are numbered 1,...
You have a pair of 4-sided dice. The four sides of each die are numbered 1, 2. 3, and 4. Each time the pair of dice is rolled, you add the numbers from each die. Out of all the possible ways the dice can land, how many of them give you a sum of 5? Number How many ways give you a sum of 8? Number What is the probability of rolling a sum of 7 with these dice? Number
2. For each of the following combinatorial problems, give a function G(x) and a value of...
2. For each of the following combinatorial problems, give a function G(x) and a value of k such that the answer to the proble is the r* coefficient of G(x) (e.g. if I had asked how many subsets of size 7 there are of a set of size 10, one answer would be "The z7 coefficient of") 2a. I ro 10 dice. Five of the dice are numbered from 1 to 6, and the remaining five numbered from 1 to...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it...
A necklace is a circular arrangement of beads which can be rotated and flipped without being considered a different arrangement. For example, there is only one necklace strung together from three beads where all beads have different colors. a) How many different necklaces with N beads can be made with N distinct colors? b) How many different necklaces can you string together if you have to use 5 beads and up to 2 colors? c) Now suppose we can only...
3. An urn contains five white balls numbered from 1 to 5, five red balls numbered from 1 to 5 and five blue balls numbered from 1 to 5. For each of the following questions, please give your answer first in the form that reflects your counting process, and then simplify that to a number. You must include the recipes. No other explanation needed. (a) In how many ways can we choose 4 balls from the urn? (b) in how...
please illustrate each stepbof the solution so I can
understand
thank you
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if two colors (red and blue) are available? (b) How many ways, if additionally we want that at most two numbered vertices are painted red?
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint...
You have a pair of 4-sided dice. The four sides of each die are numbered 1, 2. 3, and 4. Each time the pair of dice is rolled, you add the numbers from each die. Out of all the possible ways the dice can land, how many of them give you a sum of 5? Number How many ways give you a sum of 8? Number What is the probability of rolling a sum of 7 with these dice? Number
2. For each of the following combinatorial problems, give a function G(x) and a value of k such that the answer to the proble is the r* coefficient of G(x) (e.g. if I had asked how many subsets of size 7 there are of a set of size 10, one answer would be "The z7 coefficient of") 2a. I ro 10 dice. Five of the dice are numbered from 1 to 6, and the remaining five numbered from 1 to...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it...
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