Since the blue and the red boxes have to get the same number of balls for all , it is enough to count the number of ways there are to distribute balls into 6 red boxes. Once this is done the same configuration can be duplicated on the blue boxes. Since the balls are all identical, there is no need to count the permutation of the balls.
Now look at the number of ways we can distribute 75 balls into 6 different red boxes. To do this, think of the balls as arranged in a straight line. To partition, we need to pick 5 gaps between the balls. Since blanks are allowed we need to add extra blanks (4 of them) before and after the line. There are blanks and we have to choose 5 of them.
Hence the number of ways to partition is .
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6...
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.
You have 6 red balls, three of which are identical and the other three are distinct and different from the previous three, 4 distinct yellow balls, 5 identical blue balls. You want to select 7 balls to make a gift bag. How many different options per gift bag do you have?
18. How many ways are there to distribute k balls into n distinct boxes (k < n) with at most one ball in any box if(a) The balls are distinct?(b) The balls are identical?40. How many nonnegative integer solutions are there to the pair of equations x1 + x2 +ยทยทยท+ x6 = 20 and x1 + x2 + x3 = 7?56. How many ways are there to distribute 20 toys to m children such that the first two children get...
There are 15 red balls and 10 blue balls. 1) How many ways are there to choose one ball to be placed on a chair and one ball to be placed on a desk? (My original answer was 600) 2) How many ways are there to choose one ball to be placed on a chair and one ball to be placed on a desk if both balls cannot be the same color? (My original answer was 150) 3) How many...
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. 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...
You have 6 red balls, three of which are identical and the other three are distinct and different from the previous three, 4 distinct yellow balls, 5 identical blues balls. You want to select 7 balls to make a gift bag. How may different options for the gift bag do you have?
How many ways are there to distribute 8 identical apples, 6 oranges, and 7 pears among 3 different people.. Without restriction? With each person getting at least one pair? Please explain this well, and don't write it out in chicken scratch.
(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.