Question 1160471
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<pre>

The answer is the ratio of two numbers.



The denominator is the number of all subsets of 8+5 = 13 persons, consisting of 3+2 = 5 persons;

    so; by the definition, it is the number of all combinations of 13 persons taken 5 at a time

        {{{C[13]^5}}} = {{{(13*12*11*10*9)/(1*2*3*4*5)}}} = 1287.



The numerator is the number of all subsets, consisting of 3 females and 2 males.


    We can select 3 females of 8 female students by  {{{C[8]^3}}} = {{{(8*7*6)/(1*2*3)}}} = 8*7 = 56 ways;

    We can select 2 males of 5 male students by  {{{C[5]^2}}} = {{{(5*4)/(1*2)}}} = 5*2 = 10 ways.



Finally, the probability under the question is this number


    P = {{{(56*10)/1287}}} = 0.43512 = 43.512%.      <U>ANSWER</U>
</pre>

Solved.


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On Combinations, &nbsp;see introductory 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.



On simple and simplest introductory lessons on Probability, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Simple-and-simplest-probability-problems.lesson>Simple and simplest probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability.lesson>Solving probability problems using complementary probability</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-True-False-test.lesson>A True/False test</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-multiple-choice-answers-test.lesson>A multiple choice answers test</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-probability-problems-from-the-archive.lesson>Typical probability problems from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Experimental-probability-problems.lesson>Experimental probability problems</A> 

in this site.


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