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# help with counting

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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
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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
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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