Answer:
There will be 1716 combinations of the books I can make.
Step-by-step explanation:
Out of 13 possible books, I plan to take 6 books with me on a vacation.
I have to find the collections of 6 books I can take.
Its a question of combination. Total number of books is 13 and we have to make 6 combinations out of these 13 books.
Combinations will be = [tex]^{13}C_{6}[/tex] or ( 13, 6 )
[tex]^{13}C_{6}[/tex] = [tex]\frac{13!}{((13-6)!6!}[/tex] = [tex]\frac{13!}{7!6!}[/tex]
= [tex]\frac{13\times 12\times 11\times 10\times 9\times\times 8\times 7!}{7!6!}[/tex]
= [tex]\frac{13\times 12\times 11\times 10\times 9\times\times 8\times 7!}{6\times 5\times 4\times 3\times 2}[/tex]= [tex]\frac{1235520}{720}=1716[/tex]
There will be 1716 combinations of the books I can make.
Taking into account the definition of combination, you can take 1716 different collections of 6 books.
Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in which the order in which the elements are chosen is not taken into account and repetition is not possible.
The combination is calculated by:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.
In this case it is possible to apply a combination, not all the elements enter, the order in which the books are chosen does not matter, and they are not repeated.
Being m= 13 and n=6, the combination is calculated by:
[tex]C=\frac{13!}{6!(13-6)!}[/tex]
Solving:
[tex]C=\frac{13!}{6!7!}[/tex]
C= 1716
Finally, you can take 1716 different collections of 6 books.
Learn more about combination:
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