Question 698232: i am not sure if i am doing this right. could you please help me with this word problem?
jo's six different spiderman comics books, five different archie comic books, and four different garfield comic books are stacked in a pile. the different types of comic books are grouped together. In how many different orders can these comic books be stacked in a pile with the covers facing up and all of them facing the same direction? express your answers as a whole number
what i have done:
6 spiderman- 6*5*4*2*1=720
5 archie- 5*4*3*2*1=120
4 garfield- 4*3*2*1=24
answer i am not sure of-864 ways
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
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
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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