Question

A bookshelf contains 5 different mathematics textbooks, 4 different engineering textbooks, and 2 different history textbooks. How many different ways are there to arrange the books on a shelf?

Answer 1

Answer:

$11!$

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 !

$11! = 11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$

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!