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# you have 6 different Algebra books, 5 different Biology books, 4 different Chemistry books, and 3 different copies of the novel Dune. In how

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You have 6 different Algebra books, 5 different Biology books, 4 different Chemistry books, and 3 different copies of the novel Dune. In how many distinct ways can you arrange

a) 10 books on a shelf if exactly 4 must be Algebra books?

b) all of the books on a shelf if the copies of Dune must be on the ends?

Feb 27, 2021

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As per given by the question, there are 6 different Algebra books, 5 different Biology books, 4 different Chemistry books, and 3 different copies of the novel Dune.

Now,

(a). 10 books on a shelf if exactly 4 must be Algebra books?

here, 4 must  be algebra book,

So,

Number of ways to arrange the exactly 4 algebra books are,

4!=244!=24

Remaining box are 6, then there are,

24+6=3024+6=30

(b). all of the books on a shelf if the copies of Dune must be on the ends?

There are 3 different copies of the novel Dune.

Total number of book is 18.

So.

18p3 = 18/(18-3)!

= 4896

Hence, 4896 books on a shelf if the copies of Dune must be on the ends.

May 18, 2021