+0  
 
0
403
2
avatar

Suppose that I have 6 different books,  2 of which are math books. In how many ways can I stack my 6 books on a shelf if I do not want the math books to be at the ends?

 Jan 7, 2021
 #1
avatar+2401 
0

Hello Guest!

 

_ _ _ _ _ _

Let each of those spots represent a book. 

There are 4 spots where the math books can be, making 4*3 = 12 different placements of them.

After the placing the math books, there are 4 other books that can be placed in 4*3*2*1 ways. 

Thus, our answer is (4*3)*(4*3*2*1) = 228

 

I hope this helped. :)))

 

=^._.^=

 Jan 7, 2021
 #2
avatar+285 
-1

Another way to see this  =  total arrangements possible  less the arrangements where the math books are together

 

Total arrangements  =  6!   = 720

 

Total arrangemens where the  math books are together = they can occupy any of 5 positions....and for each of these positions, they can be arranged in two ways......and for each of these, the other books can be arranged in 4! ways  ......so we have     5 * 2! * 4!  =  10 * 24   = 240

 

So........720 −  240   =    480 ways

 Jan 7, 2021

5 Online Users

avatar
avatar
avatar
avatar