Difference between revisions of "004 Sample Final A, Problem 17"

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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Revision as of 16:19, 5 May 2015

How many ways can a committee of four people can be selected from five married couples if no committee is to include both husband-and-wife pairs? (simplify your answer to a single number)

Foundations
Answer:


Solution:

Step 1:
We can at most choose 1 person from the husband and wife pairs.
So, we have ways to pick a 4 people from each couple.
Step 2:
But, then for each couple, we could choose the husband or the wife to serve on the committee.
So, there are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 {5\choose 4} =10} ways to select a committee of four people.
Final Answer:
10

Return to Sample Exam

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