How many ways can four red balls and four blue balls be randomly placed in eight...

Question

Question

How many ways can four red balls and four blue balls be randomly placed in eight

urns that are numbered one to eight so that exactly one ball is in each urn?

math Statistics-And-Probability

Answer 1

Answer #1

This is a question of permutation.

Number of ways that 8 balls can be arranged in 8 boxes is given as 8!

We have 8 balls out of which 4 are red alike and 4 are blue alike so 8! Will be divided twice by 4! Because of repetition of alike colored balls.

Hence our required answer is 8!/(4! * 4!) = 70 ways.

Answer 2

Similar Homework Help Questions

3. An urn contains five white balls numbered from 1 to 5, five red balls numbered...

3. An urn contains five white balls numbered from 1 to 5, five red balls numbered from 1 to 5 and five blue balls numbered from 1 to 5. For each of the following questions, please give your answer first in the form that reflects your counting process, and then simplify that to a number. You must include the recipes. No other explanation needed. (a) In how many ways can we choose 4 balls from the urn? (b) in how...
There are 15 red balls and 10 blue balls. 1) How many ways are there to...

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...
Urn A contains two red balls and eight blue balls. Urn B contains two red balls and ten green balls. Six balls are drawn...

Urn A contains two red balls and eight blue balls. Urn B contains two red balls and ten green balls. Six balls are drawn from urn A and four are drawn from urn B; in each case, each ball is replaced before the next one is drawn. What is the most likely number of blue balls to be drawn? What is the most likely number of green balls to be drawn?

Four balls are to be randomly chosen from an urn containing 4 red, 5 green, and...

Four balls are to be randomly chosen from an urn containing 4 red, 5 green, and 6 blue balls. 1. Find the probability that at least one red ball is chosen? 2. Given that no red balls are chosen, what is the probability that there are exactly 2 green balls among the four balls chosen.
In an urn, there are 10 blue balls and 10 red balls. Balls are randomly selected...

In an urn, there are 10 blue balls and 10 red balls. Balls are randomly selected from the urn over and over again. Find the probability that the third blue ball is chosen on the fifth selection under the different assumptions: a) Balls are NOT returned to the urn after selection. b) Balls are returned to the urn after being selected.
In an urn, there are 10 blue balls and 10 red balls. Balls are randomly selected...

In an urn, there are 10 blue balls and 10 red balls. Balls are randomly selected from the urn over and over again. Find the probability that the third blue ball is chosen on the fifth selection under the different assumptions: a) Balls are NOT returned to the urn after selection. b) Balls are returned to the urn after being selected.

Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and...

Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and 3 blue balls. The urns are equally likely to be chosen. a) If a blue ball is drawn, what is the probability that it came from urn 1? b) If a red ball is drawn, what is the probability that it came from urn 2?
Suppose there is an urn containing 5 red, 4 white, and 11 blue balls. We drawn...

Suppose there is an urn containing 5 red, 4 white, and 11 blue balls. We drawn six balls from the urn (no replacement) (a) Find the number of ways (not the probability) of choosing a red ball, then a blue ball, then exactly 2 white balls, and finally exactly 2 blue balls. (b)Find the number of ways of choosing 2 red balls initially , then at least 3 blue balls, then a green ball. (c) Find the number of ways...
Refer to Example 4.40. An urn contains six red balls, six white balls, and six blue...

Refer to Example 4.40. An urn contains six red balls, six white balls, and six blue balls, and sample of four balls is drawn at random without replacement. Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.) b) An urn contains eight red balls, eight white balls, and eight blue balls, and sample of five balls is drawn at random without replacement. Compute the probability that the...

In how many ways can 15 red marbles and 17 blue marbles be distributed to 6...

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?