truggling with these problems, which I believe are both cases of pigeonhole principle but I am struggling to get the right answer. 1) An IT survey asks desktop computer users the following questions: -- which OS type they are using (Windows, macOS, Linux, other) -- if Windows: Windows 10, 8.1, 7 or other -- if macOS: 10.12, 10.11, lower -- if Linux: Mint, Debian, Ubuntu, other -- screen resolution used (lower, equal or higher than 1920x1080) -- whether they play games on their desktop (yes/no) How many people have to be asked to guarantee that you will find 10 with identical answers? 2) How many subsets are there of a set of 100 elements that contain at least 4 elements? You must simplify your answer until it contains only unresolved large exponential expressions of the form π‘Ž 𝑏 with a and

Frida Faulkner

Frida Faulkner

Answered question

2022-09-09

truggling with these problems, which I believe are both cases of pigeonhole principle but I am struggling to get the right answer.
1) An IT survey asks desktop computer users the following questions: -- which OS type they are using (Windows, macOS, Linux, other) -- if Windows: Windows 10, 8.1, 7 or other -- if macOS: 10.12, 10.11, lower -- if Linux: Mint, Debian, Ubuntu, other -- screen resolution used (lower, equal or higher than 1920x1080) -- whether they play games on their desktop (yes/no) How many people have to be asked to guarantee that you will find 10 with identical answers?
2) How many subsets are there of a set of 100 elements that contain at least 4 elements? You must simplify your answer until it contains only unresolved large exponential expressions of the form π‘Ž 𝑏 with a and b integers.

Answer & Explanation

William Collins

William Collins

Beginner2022-09-10Added 12 answers

For (2)
There are 2 100 subsets of a set of 100 elements (each element is either in or our of the subset). How many of them have fewer than 4 elements? ( 100 3 ) + ( 100 2 ) + ( 100 1 ) + ( 100 0 ) = 166751. So the number of subsets containing at least 4 elements is 2 100 βˆ’ 166751.
tophergopher3wo

tophergopher3wo

Beginner2022-09-11Added 5 answers

Hint for Number 1: How many different surveys are possible? i.e. what is the maximum possible number of surveys, so that any two will differ in at least one answer.
Number 2 isn't really a PHP problem.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Research Methodology

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?