Mathematics Homework Solutions
Problem
#25438

Counting

6. Eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room... (see attachment for rest of question)

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Please typeset your solutions with a math symbol editor (for example,
Latex)

For any answer you give, describe your solution process in words. NO
SOLUTION TO EVEN A SIMPLE PROBLEM SHOULD JUST HAVE ALGEBRAIC
SYMBOLS…EVERY SOLUTION NEEDS TO BE DESCRIBED IN WORDS.

For proofs, write out the proof as you normally would. Then, include an
explanation of your proof PRIMARILY IN WORDS. So you should have one
regular proof (the kind you see in textbooks), then another proof that
describes the proof mainly in words(you don’t see this that often).

NOTE: YOUR ANSWER IN EACH CASE SHOULD BE AN INTEGER; USING NOTATION OR
FACTORIALS IS NOT ACCEPTABLE AS AN ANSWER.

Solution Summary

In this solution set, eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room. There are several counting questions in this solution based on this situation.

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