A sonnet is a 14-line poem in which certain rhyming patterns are followed. The w

Question

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 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.

A. How many sonnets can be created from the 10 in the book?

B. If one of the sonnets countered in part (a) is selected at random, what is the probablity that none of its lines came from either the first or last sonnet in the book?

Explanation / Answer

How many sonnets can be created from the 10 in the book?

Each of the 14 lines has 10 possibilities in the book, so there are
10^14 = 100,000,000,000,000 (one hundred trillion) possible sonnets.

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?

Sonnets with no lines selected from the first or last sonnet in the book have only 8 possible sources for each line, so there are
8^14 = 4,398,046,511,104 of them,
and the probability of selecting one of them at random is
(8/10)^14 = 0.04398046511104

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