(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.
(1) We are given 40 identical (indistinguishable) objects and we want to distribute them among 7...
We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box is empty find the probability that box 1 contains 3 balls.
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.
1. Multiplication theorem There are 20 toys and 12 children. We want to distribute the toys to the children. In each of the cases below, count how many ways can we distribute the toys. (Hint: think, what are my boxes and how can I fill them?). Please show your work. You can leave the expressions as is, so no nieed to do the calculations (a) If cach child gets cxactly one toy. b) Every toy is given out and it...
6. A box contains 8 novels and 7 math books going to loan 6 books to a friend. How many different (a) You are book selections could your friend receive? going to loan 3 novels and 4 math books to a friend. How (b) You are many different book selections could your friend receive? (c) You are going to loan at least 13 books to a friend. How many different book selections could your friend receive? going to loan at...
Problem 4. 1. I’ve invited 6 friends over to my house, and each of them brings a cat with them. (It’s a cat party, obviously!) I decide to place the 6 distinct cats into 3 identical cat beds. In how many ways can I do this? 2. Prove the S(n, k) = S(n − 1, k − 1) + kS(n − 1, k). 3. Give an example of an onto function f : [6] → [3]. Give an example of...
In python.. If we want the computer to pick a random number in a given range say to write code for Picking a random element from a list or pick a random card from a deck, flip a coin etc. we can use Random module The Random module contains some very useful functions one of them is randrange() randrange(start, stop) Example from random import randrange for i in range (3): print ("printing a random number using randrange(1, 7)",r andrange(1, 7))...
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....
(1 point) In this problem we consider three functions / Each of them is continuous at: -0.ie.. lim f() = f(0). In order to show by the €/ definition that this is true one has to give a definition of in terms of e such that 12-01<8 = If(x) - (0) << Match these choices of 8 1.8 - 2.8 3.8= with the functions so that that choice of establishes continuity of the function (at 1-0). You can use each...
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to count the number of microstates that are compatible with a given gas macrostate, which we describe by specifying the gas's total energy u (within a tiny range of width dlu), the gas's volume V and the num- ber of molecules N in the gas. We will...
Project 7: Vehicles 1 Objective In the last couple projects, you’ve created and used objects in interesting ways. Now you’ll get a chance to use more of what objects offer, implementing inheritance and polymorphism and seeing them in action. You’ll also get a chance to create and use abstract classes (and, perhaps, methods). After this project, you will have gotten a good survey of object-oriented programming and its potential. This project won’t have a complete UI but will have a...