Question

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?

Answer #1

Ten distinct balls are distributed among ten distinct
boxes
1.find the probability that only one of these ten boxes is
empty.
2.how would your answer change if the balls were indistinct while
the boxes are distinct

STAT Question
1.We have 3 distinct balls (indexed Ball 1, Ball 2, Ball 3) and
3 distinct boxes (indexed Box 1, Box 2 and Box 3). Now randomly
assign each ball (independently of other balls) into one of the
boxes.
Fully simplify your final answer to each question into a
fraction or decimal.
Calculate the probability that no box is
empty.
Calculate the probability that no box is
empty.
Need Help ! !

STAT Question :
We have 3 distinct balls (indexed Ball 1, Ball 2, Ball 3) and 3
distinct boxes (indexed Box 1, Box 2, and Box 3). Now randomly
assign each ball (independently of other balls) into one of the
boxes.
Fully simplify your final answer to each question into a
fraction or decimal.
Calculate the probability that no box is
empty.
Calculate the probability that ONLY Box 1 is
empty.
NEED HELP !! THANKS

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.

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...

Probability question:
The number of ways to distribute 11 identical balls into 4
distinct boxes such that Box 1 has at most 3 balls and Box 2 has at
most 2 balls is?

Three balls are randomly dropped into three boxes. Assume that
any ball is equally likely to fall into each box. Specify an
appropriate sample space and determine the probability that exactly
one box will be empty.

Fact Suppose there are n distinct objects. There are (n above k)
possible ways to remove k objects. You only need to express your
answers in the “n-choose-k” notation. For the following questions,
it might be helpful to rst write down the sample space.
1. There are 4 balls. Draw 2 balls. Each pair of balls is
equally likely to be drawn. What is the probability that the
outcomes are either (1, 2) or (1, 3)?
2. There are 4...

Suppose that balls are successively distributed among 8 urns,
with each ball being equally likely to be put in any of these urns.
What is the probability that there will be exactly 4 nonempty urns
after 9 balls have been distributed?

3. [Conditional probabilities] There are three boxes, each
containing two coins. One box has two gold coins, another two
silver coins, and the third has one gold and one silver coin. One
of the three boxes is chosen at random and from that box a coin is
drawn at random. Suppose that coin happens to be gold. What is the
probability that the remaining coin in the box is also gold? Show
your work.

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