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

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<span class="exam"> 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)
 
<span class="exam"> 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)
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|-
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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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|-
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|Answer:
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|-
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|We can at most choose one person from each couple to serve on the committee.
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|}
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Solution:
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{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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|We can at most choose 1 person from the husband and wife pairs.
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|-
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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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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 2:
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|-
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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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|-
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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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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Final Answer:
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|-
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|10
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|}
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[[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

Return to Sample Exam

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