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 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? 1014 (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 eighth or the last sonnet in the book? (Round your answer to three decimal places.)

Explanation / Answer

a)

here number of sonnets =N(for each line there are 10 choices)=1*1014

b)

number of ways a sonnent does not come from 8th sonnet =914 (Asthere are 9 choice for each line)

number of ways a sonnent does not come from 10th sonnet =914 (Asthere are 9 choice for each line)

number of ways a sonnet does not come fom 8th and 10th sonnet =814

hence P(none of its line comes from 8th or last sonnet)=(914+914-814)/1014 =0.414

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