Question 1191639
.
Your sister has a book collection that consists of 20 horror novels, 15 romance novels, 
and 25 mystery novels. She randomly picks 3 books to read during a long trip. 
What is the probability that she picks one from each category?
~~~~~~~~~~~~~~


<pre>
She can select one horror book from 20 such books in 20 ways;

She can select one romance book from 15 such books in 15 ways;

She can select one mystery novel from 25 such books in 25 ways.



In all, she has 20*15*25 = 7500  such different selections satisfying the imposed condition.



To find the probability of making <U>right selection</U>, we should relate this number, 7500, to the total number of all possible triples 

from 20+15+25 = 60 books.  In all, there are  {{{C[60]^3}}} = {{{(60*59*58)/(1*2*3)}}} = 34220  such triples.


So the sough probability is  P = {{{7500/34220}}} = 0.2192 = 21.92%  (rounded).    <U>ANSWER</U>
</pre>

Solved.