Difference between revisions of "004 Sample Final A, Problem 17"
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! Foundations | ! 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: | |Answer: | ||
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| − | | | + | |We can at most choose one person from each couple to serve on the committee. |
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! Step 1: | ! 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 <math>5 \choose 4</math> ways to pick a 4 people from each couple. |
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! Step 2: | ! 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 <math>2 {5\choose 4} =10</math> ways to select a committee of four people. |
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! Final Answer: | ! Final Answer: | ||
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| − | | | + | |10 |
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']] | [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 14:27, 11 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 |
|---|
| 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 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 ways to select a committee of four people. |
| Final Answer: |
|---|
| 10 |