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# plz help i need this one last question am stuck

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200
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You have 5 Math books, 4 History books, and 3 Science books.

1 question, How many ways are there to arrange the books on a book shelf?

ans= 479001600 i want to know how they got the first question number plz help

2question, How many ways are there to arrange the books on a book shelf if the books from each category must stay together?
ans=103680

Sep 17, 2019
edited by Arizona115970  Sep 17, 2019
edited by Arizona115970  Sep 17, 2019
edited by Arizona115970  Sep 17, 2019

#2
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1 - The answer given to you: 479001600 comes from: [5 + 4 + 3] = 12! =479,001,600

2 - Also the answer given to you: 103680 comes from: 5! x 4! x 3! =17,280. Since the 3 categories can be arranged in 3! = 6 different way, then:17,280 x 6 =103,680 ways.

Sep 17, 2019

#1
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$$\text{I assume the books of a given type are indistinguishable}\\ \text{You have 12 books. If they were all distinguishable there would be 12! arrangements}\\ \text{As they are not we have to reduce this number by the number of permutations of each type}\\ N = \dfrac{12!}{5!\cdot 4!\cdot 3!} = 27720$$

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Sep 17, 2019
#2
+1

1 - The answer given to you: 479001600 comes from: [5 + 4 + 3] = 12! =479,001,600

2 - Also the answer given to you: 103680 comes from: 5! x 4! x 3! =17,280. Since the 3 categories can be arranged in 3! = 6 different way, then:17,280 x 6 =103,680 ways.

Guest Sep 17, 2019
#3
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you're wrong

Rom  Sep 17, 2019