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?

Guest Jan 7, 2021

#1**0 **

Hello Guest!

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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. :)))

=^._.^=

catmg Jan 7, 2021

#2**-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

hihihi Jan 7, 2021