Problem 3: Twenty workers were assigned to two construction sites with the first

Question

Problem 3: Twenty workers were assigned to two construction sites with the first site requiring six workers, and the second requiring fourteen workers. The first site had particularly unpleasant conditions. Management claimed that the six workers assigned to the first site were randomly selected out of twenty. However, all five members of a particular ethnic group were assigned to the first site. If the workers were assigned randomly, then what is the probability of all five members of the particular ethnic group being assigned to the first site? 13 points

Explanation / Answer

total number of ways of assigning 2 groups of 14 and 6
= 20C6

now number of ways 5 men of particular group is assigned to first site
= 15C1        {note that we to select 6th member for first site from remaining 15 members}

hence required probability
= 15 / 20C6

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