Question

Assume there are 100,000 unique web pages* and answer the following:
5a) A Google search returns a first page of 20 results each in a ranked order. How many possible first page rankings are there for the 100,000 web pages?
BONUS: 5b) How many rankings of 20 pages are there if two of the 100,000 pages are duplicates. Hint: You might need to use the rule of sum.
5c) In Information Retrieval, a field of Data-Mining for correctly returning search results in domains such as web search, company databases, or ranking threats, only a very small portion of candidates are actually relevant to a query. For example, maybe only 10 webpages of the total 100,000 are relevant to the search query "Canucks' playoff chances". What is the probability that all 10 of these pages are returned in the first page of google results under the equal likelihood assumption?
5d) Information Retrieval uses preprocessing to only consider a small portion of candidate web pages. For example, usually only two thousand pages with certain matching keywords are ever possibly returned in Google's top results. What is the probability that all 10 relevant pages are in the first page of these 2000 options under equal likelihood?
5e) How would your answer 5d change if 100 candidate pages were returned instead of 2000?

Answer 1

5a)->

First, there are choosing 20 out of 100000 this will give us,

and then we will shuffle the selected 20 results, this will give us,

So,

The final answer is,

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NOTE:- For answers to other questions, ask those questions separately.