Respuesta :
Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.
As per the question statement, Hector has shortlisted 11 documentaries and 15 foreign films, from which he wants to rent any 4 movies.
We are required to calculate the total of number of combinations of 4 movies from his above mentioned shortlist.
Total number of movies Hector has shortlisted = (11 + 15) = 26.
That is, we will have to calculate the total of number of combinations of 4 movies, Hector can rent from a lot of 26 movies.
Now, we need to know the formula of combination which goes as [tex][nCr=\frac{n!}{r!(n-r)!} ][/tex],
When "r" objects are to be selected from a set of "n" objects, such that order of selection does not matter.
Here, (n = 26) and (r = 4), and using these values in the above mentioned equation of nCr, we get
[tex]26C4=\frac{26!}{4!(26-4)!} =\frac{26!}{4!*22!}=\frac{22!*23*24*25*26}{24*22!}=(23*25*26)=14950[/tex]
That is, Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.
- Combination: In mathematics, combination is a method of selecting items from a set, where the order of selection does not matter.
To learn more about Combinations, click on the link below.
https://brainly.com/question/8561440
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