In how many ways can n identical balls be distributed
into k bins such that each bin contains
at least two balls. Assume that n ≥ 2k.
In how many ways can n identical balls be distributed into k bins such that each...
How many ways can n identical balls be distributed into k bins such that each bin contains at least two balls? Assume that n ≥ 2k. Please type your answer or use neat handwriting.
In how many ways can 22 identical bottles of soda be distributed among four people, disregarding the order of distribution, so that each person gets at least one bottle? 34.
Suppose we toss balls into 5 bins until some bin contains two balls. Each toss is independent, and each ball is equally likely to end up in any bin. What is the expected number of ball tosses?
Use simulations to analyze the behavior of hashing with chaining using the balls-and-bins simulations. Assume being given n balls and m bins, and you are throwing n balls uniformly randomly into m bins. You need to answer the following questions for various combinations of values of n and m: After throwing n balls into m bins: 1) How many (what fraction of m) of bins were empty? (MIN,MAX and AVERAGE --- explanation below) 2) How many bins (what percentage of...
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...
1) What is the probability of having every bin filled with at least one ball if n balls are distributed randomly in to m bins ? Do all case m < n, m = n , m > n 2) what is the probability of having two aces and 3 black cards in choosing five cards from a shuffled deck? 3 a) The probability of success is p, failure 1-p what is the probability of having at least k success...
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...
In how many ways can 15 red marbles and 17 blue marbles be distributed to 6 children if each child is to receive at least one blue marble and at least 2 red marbles? In how many ways can 32 different books be placed on four shelves so that there is at least one book on each shelf?
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls are drawn in succession. a) what is the probability that m is the largest number drawn? b) what is the provability that the largest number drawn is less than or equal to m?