Question 698232
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You have started down the correct path, but...


For each of the 720 ways that you can arrange the Spiderman books, there are 120 ways to arrange the Archie books, so just considering Spiderman and Archie, you have 720 TIMES 120 ways and then either the Archie books group could be on the top of the pile or the Spiderman books could be on top of the pile so you have another factor of 2.


Throwing in the Garfield books you have 720 ways to arrange the Spideys times 120 ways to arrange the Archies times 24 ways to arrange the Garfields times 6 ways to arrange the three groups.


Altogether 720 * 120 * 24 * 6 = 12,441,600.


Compare to the arrangements if you DON'T keep them in groups:  15! = 1,307,674,368,000.  Throw in another book and you have the national debt.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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