Question 1136905
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            I will solve the problem (A) only.



<U>Solution 1.</U>


<pre>
In how many ways the manager can select 3 applicants from 10 persons ?

In  {{{C[10]^3}}} = {{{(10*9*8)/(1*2*3)}}} = 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  {{{C[5]^3}}} = {{{(5*4)/(1*2)}}} = 10.

It is the number of favorable elements.



Now the probability under the question is  P = {{{favorable/all}}} = {{{10/120}}} = {{{1/12}}} = 0.08333... = 8.333%.     <U>ANSWER</U>
</pre>

Solved.


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On Combinations, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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.



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<U>Solution 2.</U>


<pre>
The probability that the first applicant randomly selected by the manager has a college degree is  {{{5/10}}} = {{{1/2}}};


same about the second applicant is  {{{4/9}}};


same about the third applicant is  {{{3/8}}}.


The product of these probabilities is  {{{(1/2)*(4/9)*(3/8)}}} = {{{12/144}}} = 0.08333... = 8.333%,


and you get the same answer as in the <U>Solution 1</U>.
</pre>



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