Question

The Wikipedia article on the length of dictionaries suggests there are 171,476 unique words in the English language. How many unique books are possible of length 0, 1, 2, 3, ..., k? Assuming we have a team of 1 billion very fast typists who each write unique books 1 billion times per second, rounded up to the nearest million years, how long will it take this team to write all possible texts of 6 or fewer words?

Answer 1

806 million years

Explanation:

From the information given:

Firstly, we need to determine the no. of ways we can choose n many words in the dictionary & array them in
`(^(171476)_(n)) * n!` ways.

Thus, the no. of unique books possible of length till K is:

`\sum \limits^k _(n=0) ( ^(171476)_(n)) * n! \\ \\ = \sum \limits ^k_(n=0) (171476!)/((171476-n)!)`

where K = 6, we have the value to be:

= 25420530373932821216635722990977

Thus, the time required to write all possible texts of 6 is:

= (25420530373932821216635722990977)/10⁶

≅ 806 million years.