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

Arizona115970 Sep 17, 2019

edited by
Arizona115970
Sep 17, 2019

edited by Arizona115970 Sep 17, 2019

edited by Arizona115970 Sep 17, 2019

edited by Arizona115970 Sep 17, 2019

edited by Arizona115970 Sep 17, 2019

#1**0 **

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

.Rom Sep 17, 2019