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A construction job needs 10 workers . 5 of the workers will go to site A, 3 of the workers will go to site B , and 2 of the workers will go to site C. a. What is the number of ways can the 10 workers be divided into the 3 sites? b. Suppose that three of these 10 “workers ” are actually QUALITY investigators. What is the probability that each of the job sites is assigned one of the quality investigators given the fact that the assignment of these workers is random?

A construction job needs 10 workers . 5 of the workers will go to site A, 3 of the workers will go to site B , and 2 of the workers will go to site C. a. What is the number of ways can the 10 workers be divided into the 3 sites? b. Suppose that three of these 10 “workers ” are actually QUALITY investigators. What is the probability that each of the job sites is assigned one of the quality investigators given the fact that the assignment of these workers is random?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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A construction job needs 10 workers . 5 of the workers will go to site A, 3 of the workers will go to site B , and 2 of the workers will go to site C.

a. What is the number of ways can the 10 workers be divided into the 3 sites?

b. Suppose that three of these 10 “workers ” are actually QUALITY
investigators. What is the probability that each of the job sites is assigned one of
the quality investigators given the fact that the assignment of these workers is random?

 

Expert Solution
Step 1: Write down the given information

Total 10 workers

N = 10 , 

Site A (n1) = 5 workers

Site B (n2) = 3 workers 

Site C (n3) = 2 workers 

To choose n objects from N objects : 

Ways = NCn = N! / (n!*(N-n)!) 

Here : 

N! =N*(N-1)*(N-2)*....1 

Probability = favorable / total 

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