Statistics question involving combinations and groups

In summary, the conversation is about a labor dispute regarding the distribution of twenty laborers to four different construction jobs. The dispute arose over an alleged random distribution of the laborers to the jobs, which resulted in all four members of a particular ethnic group being assigned to job 1. The question asks for the probability of an ethnic group member being assigned to each job group and the probability of no ethnic group member being assigned to the fourth group. The suggested method to solve the problem is to count the number of ways the laborers could be assigned and divide by the total number of ways to assign them. In part (a), this involves choosing an ethnic group member and non-ethnic group members for each job group. Part (b) is
  • #1
willworkforfood
54
0
I'm not sure where to start on this one at all, very confused. I don't want anyone to do the entire problem for me just point me in the right direction. I know how to compute probability from simple random events but this question just confuses the heck out of me :(

Question:

A labor dispute has arisen concerning the alleged distribution of twenty laborers to four different construction jobs. The first job (considered to be abominable employment) required six laborers; the second, third and fourth utilized four, five and five laborers, respectively.

The dispute arose over an alleged random distribution of the laborers to the jobs which placed all four members of a particular ethnic group (there are only 4 members of this ethnic group out of the 20) on job 1.

a)What is the probability that an ethnic group member is assigned to each one of the job groups?

b)What is the probability that NO ethnic group member is assigned to the fourth group?
 
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  • #2
What have ypu done on this yourself? What are your thoughts?
 
  • #3
I don't know where to start
 
  • #4
In a, you want to count the number of ways that the laborers could be assigned in such a manner, and then divide by the total number of ways to assign them to jobs.

For the first group, (considering order unimportant), you must:
1. Choose an ethnic group member, of which there are 4.
2. Choose five non-ethnic group members, of which there are 16.

Now for the second group, (order unimportant), you must:
1. Choose an ethnic group member, of which there are how many?
2. Choose three non-ethnic group members, of which there are how many?

b is quicker but you have to realize something about which groups you can ignore and why.
 
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1. What is a combination in statistics?

A combination in statistics refers to the number of ways in which a group of objects can be selected without considering the order. It is a way to calculate the number of unique groups that can be formed from a larger set of objects.

2. How is a combination different from a permutation?

A combination differs from a permutation in that the order of selection does not matter in a combination, while it does matter in a permutation. In other words, a combination considers the selection of objects as a group, while a permutation considers the order in which they are selected.

3. What is the formula for calculating combinations?

The formula for calculating combinations is nCr = n! / (r! * (n-r)!), where n represents the total number of objects and r represents the number of objects being selected.

4. How can combinations be used in real-life scenarios?

Combinations can be used in various real-life scenarios, such as in lottery games, where the order of numbers does not matter. They can also be used in creating unique combinations for passwords or security codes.

5. What is the purpose of using combinations in statistics?

The purpose of using combinations in statistics is to determine the number of possible outcomes or combinations in a given scenario. It is a useful tool for making predictions and analyzing data in various fields such as finance, economics, and social sciences.

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