Question

9 different balls are distributed to 4 different boxes, where each box can contain at most one ball. Empty boxes are allowed, that it is possible that only one box has one ball, but the other boxes don’t have any balls. Find the possible number of ways for the distribution.

Answer #1

Suppose 5 distinct balls are distributed into 3 distinct boxes
such that each of the 5 balls can get into any of the 3 boxes.
1) What is the Probability that box 1 has exactly two balls and
the remaining balls are in the other two boxes.
2) What is the probability that there is exactly one empty
box?

How many ways can be distributed to the box of (n+1)
different balls provided that "no box remains empty".

In how many ways can you distribute 10 different balls into 4
different boxes, so there's no box with exactly 3 balls?

Box 1 contains 4 red balls, 5 green balls and 1 yellow ball.
Box 2 contains 3 red balls, 5 green balls and 2 yellow
balls.
Box 3 contains 2 red balls, 5 green balls and 3 yellow
balls.
Box 4 contains 1 red ball, 5 green balls and 4 yellow balls.
Which of the following variables have a binomial
distribution?
(I) Randomly select three balls from Box 1 with replacement. X =
number of red balls selected
(II) Randomly...

Find the number of ways to distribute 15 balls of different
colors, 20 different books and 7 bananas in five identical boxes
such that in each box there are at least one ball, one book
and one banana.

We randomly place 200 balls independently in 100 boxes in the
most natural uniform way. That is, each ball is placed
independently from the rest of the balls in such a way that the
probability to put it into the i-th box is one-percent (1 ≤ i ≤
100). Let X denote the number of empty boxes at the end. What is
the expected value of X? I also want the numerical value.

We are given n distinct balls and m distinct boxes. m and n are
non-negative integers. Every ball must be placed into a box, but
not every box must have a ball in it. Each box can hold any number
of balls. Let's also assume that the order in which we put
the balls into the boxes does matter. (Ex: assume we have
2 balls, a and b, and 3 boxes, 1 2 and 3. two distinct
distributions would be...

1. You have three boxes labelled Box #1, Box #2, and
Box #3. Initially each box contains 4 red balls
and 4 green balls. One ball is randomly selected from
Box #1 and placed in Box #2 Then one ball is randomly selected from
Box #2 and placed in Box #3. Then one ball is randomly selected
from Box #3 and placed in Box #1. At the conclusion of
this process, what is the probability that that each box has the
same number of...

Eight balls, each marked with different whole number
from 2 to 9, are
placed in a box. Three of balls are drawn at random (with
replacement) from
box.
i. What is the probability that the ball with the number 5 is
drawn?
ii. What is the probability that the three numbers on the balls
drawn are odd?
iii. What is the probability of that the sum of the three numbers
on the disc is odd.
iv. What is the probability...

Two balls are chosen at random from a closed box containing 9
white, 4 black and 2 orange balls. If you win $2 for each black
ball selected but lose $1 for each white ball selected, and letting
X stand for the amount of money won or lost, what are the possible
values of X and what are the probabilities associated with each
X?
What is the expected value of your winnings? (Note: round to the
nearest dollar)
A. Lose...

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