Question

Winston has 50 books but his bookshelf can hold only 40 books. (a) In how many ways can Winston arrange 40 of his books on his bookshelf? (b) How many of the arrangements in part (a) include Winston’s ten textbooks?

Answer #1

(a) The first space of the bookshelf can hold any one of 50
books and this can be done in 50 ways, the second space of the
bookshelf can hold any one of remaining 49 books and this can be
done in 49 ways and so on. Therefore, 40 spaces of the bookshelf
can hold by 50 books in **50P40** ways.

(b) If 10 textbooks are included, then these 10 textbooks can
hold in 40 spaces of the bookshelf in 40P10 ways. Now, remaining 40
books can hold in remaining 40 - 10 = 30 spaces of the bookshelf in
40P30 ways. Hence, the required number of arrangements is
**40P10 x 40P30** .

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