MathAdmin: Created page with " 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..."

2015-06-01T05:50:44Z

Created page with "<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..."

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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)
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|What is the maximum number of people we can choose from each couple to serve on the committee?
|-
|Answer:
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|We can at most choose one person from each couple to serve on the committee.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! 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.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
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|But, then for each couple, we could choose the husband or the wife to serve on the committee.
|-
|So, there are <math>2 {5\choose 4} =10</math> ways to select a committee of four people.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|10
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 17 - Revision history

MathAdmin: Created page with " 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..."