2. Consider the problem of counting the ways to distribute 31
identical objects into 6 boxes with at least objects in each
box.
a) Model this problem as an
integer-solution-of-equation-problem.
b) Model this problem as a certain coefficient of a generating
function.
c) Solve this problem.
The answer is a) e1+. . +e6=31, ei>=3;
b) (x^3 + x^3...)^6, coef x^31;
c) C(13+6-1,13);
Please show me how to get the answer, thanks. It's for my midterm, so it's important.

2. Consider the problem of counting the ways to distribute 31 identical objects into 6 boxes...
(1) We are given 40 identical (indistinguishable) objects and we want to distribute them among 7 distinct (distinguishable) boxes such that the box 1 must contain at least 3, and at most 10 objects. Use generating function to find the number of ways to do that.
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
Consider the following problem: How many ways are there to paint 10 identical houses on a street with five colors if at most three houses can be painted blue, at most three can be painted green, at most three can be painted beige, and no constraint is placed on the other two colors, brown and gray? A student claims that the generating function for this problem is g(x) = (1 + x +x2 + r3)3(1 + x + r2 +...
guided exercise 11, pg. 225 a. evaluate 31. 31 = 3, 2, 1 = 6 b. in how many different ways can three objects be arranged in order? how many choices do you have for the first position? for the second nd position? for the third position? you have three choices for the first pos. two for the second pos. and one for the third pos. by the multiplication you have (3) (2) (1) = 31 = 6 arrangements
PartB (COMBINATORICS) -LEAVE ALL ANSWERA IN TERMS OF C(n,r) or factorials, Q4(a)(i ) In how many ways can you arrange the letters in the word INQUISITIVE? in how many of the above arrangements, U immediately follows Q? Q4. (b)Su next semester. Your favorite professor, John Smith, is teaching 2 courses next semester and therefore ppose you are a math major who is behind in requirements and you must take 4 math courses you "must" take at least one of them....
Question #3 please with some explanations. Thank you!
E - 21% O Tue 10:16 PM Q 2017.pdf (page 1 of 3) @ Q Search • Know what the symbol [x4] P(x) means. Exercises A. Handout Questions In the questions below 'closed form' means writing the generating function not as an infinite series using "...", but writing it in terms of rational functions. For example, I is the closed form of 1+2++ ... 1. For each equation, express the number of...
hi i am struggling with this problem, thanks
6. Consider a sample X1, ... ,X, U(0,0) and answer following questions. (a) Suggest a reasonable estimator of 8 and explain. (b) Define Y = max(X1,..., X.). Note that Y is also a random variable since it is a function of random variables. Derive a probability of density function of Y. fy(). (Hint: P(Y < y) = P(X1 Sy, X, Sy...,X, Sy); X1,..., X, are independent; Relationship between cdf and pdf for...
Q1 (30 points) Consider Problem 11.45, Page 637. Please note that for this problem the data will be entered in R as follows: #Enter data on x = Dose Level of Drug, and y = Potency of Drug (Problem 11.45, page 637) x<-c(2, 2, 2, 4, 4, 8, 8, 16, 16, 16, 32, 32, 64, 64, 64) y<-c(5, 7, 3, 10, 14, 15, 17, 20, 21, 19, 23, 29, 28, 31, 30) For this problem, answer the following questions. In...
M5 Problem Set Score: 43.5/67 37/41 answered 6 VOC Question 31 < > B0/2 pts 5399 Details An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 26 students in her class and their performance is independent, what is the probability that at least one student gets an A? Round your answer to four decimal places. Question Help: Message instructor Submit Question M5 Problem Set 6 VO ......