2. For each of the following combinatorial problems, give a function G(x) and a value of k such that the answer to the...
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...
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2. A b ox 3. Find a1e for each of the following generating functions:
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
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...
Calculate each of the following events (1) A box of 50 light bulbs contains 3 defectives. If 5 bulbs are sampled at random from this box (without replacement), find the probability that the sample contains no defectives (2) A drawer of socks contains seven identical red socks, eight identical blue socks and nine identical green socks. Two socks are randomly picked out in the dark. What is the probability that they match? (3) Thirty people are gathered in a room....
Anonymous please do not answer this question, your answer has been wrong twice this question does not ask for probability as an answer. This is an advanced counting methods problem please do not answer with probabilities. The question is: A deck of cards consists of 3 identical Red cards, 3 identical Blue cards, 3 identical Yellow cards, and 3 identical Green cards. The cards are shuffled. Three cards are selected and the result is recorded. The three cards are returned...
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...