Respuesta :
Answer:
[tex]11![/tex]
Step-by-step explanation:
Since there are no restrictions, the books can be arranged in any order.
there are 11 books in total.
5+4+2 = 11.
hence, the short answer is: 11 !
[tex]11! = 11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1[/tex]
an explanation for this is:
if we have 11 spaces in the shelf to put the books in
_ _ _ _ _ _ _ _ _ _ _
how many available spaces do I have to put the 1st book in? 11
hence i'll write 11 for the first place.
11 _ _ _ _ _ _ _ _ _ _
now, how many available spaces do I have to put the 2nd book in? since one book is already placed, i have 10 remaining spaces. hence i'll put 10 in the 2nd place.
11 10 _ _ _ _ _ _ _ _ _
i'll continue this until i have no books left. I'll do the last one here.
how many spaces will i have if i have placed all book in the shelf but one?
11 10 9 8 7 6 5 4 3 2 _
ofcourse, I will have only one space left! hence, i'll write
11 10 9 8 7 6 5 4 3 2 1
finally, once i'm done with this. I'll multiply all the numbers to get my answer for all the possible arrangements to place the books in the shelf.
a shorter way to write all these multiplications is : 11!
