Statistics question involving combinations and groups

willworkforfood

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?

HallsofIvy

What have ypu done on this yourself? What are your thoughts?

willworkforfood

I don't know where to start

0rthodontist

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.