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 .