Extremely hard stats question?

Question

In "The art of the shakespear;s Sonnets" author Helen Vendler noted that each of the 14 lines of Sonnet 20 (One of 154 sonnets written by shakespear) includes the letters of the word "hues" and/or the letters of the word "hews"
A-Suppose that 154 monkeys sitting at 154 keyboards pounded out one sonnet a piece, each sonnet consisting of 14 lines of 36 alphabet letters each, with each letter equally likely. What is the probability that in at least one of the sonnects, every line includes teh letters of the word "hues" and/or the letters of the words "hews"

Answer 1

My first answer is "very slim."

First off: how many different one line strings can the monkeys type? 26 characters in the English language, so there are 26^36 possible strings of random characters.

What is the chance of typing a 36 character string with the letters “hews" in it? There are four letters which can be distributed amongst any of the 36 positions, so there are 36C4 ways to do this (where nCk is the binomial coefficient). The remaining 32 positions can be filled with any letters, including duplicates of “hews” so there are 26^32 ways to do that. Total number of strings with “hews” in it: 36C4*26^32.

Probability of typing “hews” randomly in a single line: p=36C4*26^32/26^36

Probability of typing “hews” randomly in each of 14 lines: p^14

Probability of 154 monkeys doing it (if they have one try): 154*p^14.

This is approximately 5.384476415*10^-11 or one chance in 19 billion.

Yup, pretty slim.