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I will solve the problem (A) only.
Solution 1.
In how many ways the manager can select 3 applicants from 10 persons ?
In = = 120 ways.
It is the number of combinations of 10 items taken 3 at a time.
At the same time, it is the number of elements in the entire space of events.
How many triples exist consisting of applicants with the college degree ?
They all are selected from the sub-set of 5 applicants having college degree.
Hence, the number of such triples is = = 10.
It is the number of favorable elements.
Now the probability under the question is P = = = = 0.08333... = 8.333%. ANSWER
Solved.
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On Combinations, see the lessons
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- OVERVIEW of lessons on Permutations and Combinations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
/\/\/\/\/\/\/\/
Solution 2.
The probability that the first applicant randomly selected by the manager has a college degree is = ;
same about the second applicant is ;
same about the third applicant is .
The product of these probabilities is = = 0.08333... = 8.333%,
and you get the same answer as in the Solution 1.
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