It has been said* that “set to strum unintelligently on the typewrites for millions of years, would be bound in time to write all the books in the British Museum.” This statement is nonsense, for it gives a misleading conclusion about very, very large numbers, could all the monkeys in the world have typed out a single specified book in the age of the universe?
Suppose that 1010 monkeys have been seated at typewrites throughout the age of the universe, 1018 s. this number of monkeys is about three times greater than the present human population of the earth. We suppose that a monkey can hit 10 typewrites keys per second. A typewriter may have 44 keys: we accept lowercase letters in place of capital letters. Assuming that Shakespear’s Hamlet has 105 characters, will the monkeys hit upon Hamlet?
(a) Show that the probability that any given sequence of 105 characters typed at random will come out in the correct sequence (the sequence of Hamlet) is of the order of

(1/44)100000 = 10–164345

Where we have used log10 44 = 1.64345.
(b) Show that the probability that a monkey-Hamlet will be typed in the age of the universe is approximately 10–164316. The probability of Hamlet is therefore zero in any operational sense of an event, so that the original statement at the beginning of this problem is nonsense: one book, much less a library, will never occur in the total literary production of the monkeys