Question

Put 5 distinguishable balls in 4 boxes. List all the possibilities of different arrangements of balls in 3 boxes and find the most probable distribution.

Answer #1

According to the question, we have 5 balls to be placed in 3 boxes where no box remains empty.

Hence, we can have the following kinds of distributions:

- Firstly, where the distribution will be (3,1,1) that is, one
box gets three balls and the remaining two boxes get one ball each.
- No. of ways to choose the box which gets 3 balls = 3 (since, 3 boxes are there).
- No. of ways to select 3 balls out of 5 is =
- No. of ways to distribute rest of the balls =2.
- Total no. of ways =60

2. Secondly, where the distribution will be (1,2,2) that is, one box gets one ball and the remaining two boxes get two balls each.

- No. of ways to select 1 ball out of 5 is =
- No. of ways to choose the box which gets 1 balls = 3 (since 3 boxes are there).
- No. of ways to select 2 balls out of remaining 4 to go in the second box is = .
- Total no. of ways = 90

Total:60+90=150.

9 different balls are distributed to 4 different boxes, where
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In how many ways can you distribute 10 different balls into 4
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Probability question:
The number of ways to distribute 11 identical balls into 4
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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
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Box 3 contains 2 red balls, 5 green balls and 3 yellow
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Box 4 contains 1 red ball, 5 green balls and 4 yellow balls.
Which of the following variables have a binomial
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(I) Randomly select three balls from Box 1 with replacement. X =
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Question 5 (1 point)
Box1: 5 green balls, 4 red balls, 5 blue
balls
Box2: 0 green balls, 4 red balls, 7 blue
balls
Experiment: Select one of the two boxes with uniform random
probability, and draw two balls from the selected box. Record the
box number as the r.v. i, and the colors of the two balls as
b1, b2.
Compute P(b1 = green )
[Round to 3 digits after decimal point]
Your Answer:

Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
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List the possible values for X and then find the entire probability
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balls. If the balls are removed from the box one at a time, in how
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Please write clearly so I can study from it! Try not
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i need to have this done soon. Thank You! :)
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balls. A ball is picked, its color recorded and returned to the
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