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
|
| What is the maximum number of people we can choose from each couple to serve on the committee?
|
| Answer:
|
| We can at most choose one person from each couple to serve on the committee.
|
Solution:
| Step 1:
|
| We can at most choose 1 person from the husband and wife pairs.
|
| 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.
|
| 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.
|
Return to Sample Exam