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
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| What is the maximum number of people we can choose from each couple to serve on the committee?
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| Answer:
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| We can at most choose one person from each couple to serve on the committee.
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Solution:
| Step 1:
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| We can at most choose 1 person from the husband and wife pairs.
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| So, we have 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 5 \choose 4}
ways to pick a 4 people from each couple.
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| Step 2:
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| But, then for each couple, we could choose the husband or the wife to serve on the committee.
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| So, there are Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 2{5 \choose 4}=10}
ways to select a committee of four people.
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