A sonnet is a 14-line poem in which certain rhyming patterns are followed. The writer Raymond Queneau published a book containing just 10 sonnets, each on a different page. However, these were structured such that other sonnets could be created as follows: the first line of a sonnet could come from the first line on any of the 10 pages, the second line could come from the second line on any of the 10 pages, and so on (successive lines were perforated for this purpose). a. How many sonnets can be created from the 10 in the book? b. If one of the sonnets counted in part (a) is selected at random, what is the probability that none of its lines came from either the first or the last sonnet in the book?

Answer : Step 1 : From the given problem a sonnet is a 14-line poem in which certain rhyming patterns are followed. The writer Raymond Queneau published a book containing just 10 sonnets, each on a different page. a). We have to find how many sonnets can be created from the 10 in the book. Each of the 14 lines has 10 possibilities in the book. There is a choice of 10 first lines, 10 second lines, etc : 10x10x10x... for all 14 lines 14 So there are 10 . 14 10 = 100,000,000,000,000 (one hundred trillion) possible sonnets. Therefore 10 sonnets can be created from the 10 in the book.