Question

In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books.
(a) How many ways can you select and arrange 10 of the 17 books on the shelf? Notice that here we will allow the books to end up in any order. Explain.
(b) How many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author? Explain.

Answer 1

Answer:

19448 ways

70572902400 ways

Step-by-step explanation:

(a)

To arrange 17 books on a shelf from a possible we use the combination formula :

nCr = n! ÷ (n-r)!r!

17C10 = 17! ÷ 7! 10!

17C10 = 19448 ways

To arrange the books in alphabetical order :

2)

In question, 2, the order of arrangement matters ; hence, we use permutation ;

nPr = n! ÷ (n-r)!

17P10 = 17! ÷ (17 - 10)! = 17! ÷ 7!

17P10 = 70572902400