Mr. Reader has six different Spiderman comic books, five different Archie comic books and four different Garfield comic books. When stacked, all of the Spiderman comic books are grouped together, all of the Archie comic books are grouped together and all of the Garfield comic books are grouped together. In how many different orders can these 15 comic books be stacked in a pile with the covers facing up and all of them facing the same direction? Express your answer as a whole number.

Question

Mathematics

Clare Rogers

10 May, 07:29

Mr. Reader has six different Spiderman comic books, five different Archie comic books and four different Garfield comic books. When stacked, all of the Spiderman comic books are grouped together, all of the Archie comic books are grouped together and all of the Garfield comic books are grouped together. In how many different orders can these 15 comic books be stacked in a pile with the covers facing up and all of them facing the same direction? Express your answer as a whole number.

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Answers (1)

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Cailyn Wheeler · Answer 1

12,441,600 ways

Step-by-step explanation:

We have 6! ways of arranging the different Spiderman comics. We also have 5! ways of arranging the different Archie comics, and we have 4! ways of arranging the different Garfield comics. Since we have 3 different items, we have 3! ways of arranging them. We also have 1 ways of arranging the covers to face up and 1 way for them to face the same direction. So, the total number of ways of arranging the comics in a stacked pile with covers facing up and in the same direction is 3!6!5!4! * 1 * 1 = 12,441,600 ways