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 13:27, 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 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.
Final Answer:
10

Return to Sample Exam

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