Difference between revisions of "004 Sample Final A, Problem 18"

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(Created page with "<span class="exam"> Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)")
 
 
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<span class="exam"> Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)
 
<span class="exam"> Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (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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|If there are n teams, how many ways can first prize be awarded?
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|-
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|Answer:
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|-
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|Each team could win first place. So, there are n ways that first prize can be awarded.
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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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|There are 10 ways that first prize could be awarded.
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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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|After choosing a first place winner, there are 9 ways that second prize could be awarded.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 3:
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|-
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|After choosing both a first and second place winner, there are 8 ways that third prize could be awarded.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 4:
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|-
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|So, the total number of ways first, second, and third prizes can be awarded is <math>10*9*8=720</math>.
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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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|<math>720</math>
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|}
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 14:28, 5 May 2015

Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)

Foundations
If there are n teams, how many ways can first prize be awarded?
Answer:
Each team could win first place. So, there are n ways that first prize can be awarded.


Solution:

Step 1:
There are 10 ways that first prize could be awarded.
Step 2:
After choosing a first place winner, there are 9 ways that second prize could be awarded.
Step 3:
After choosing both a first and second place winner, there are 8 ways that third prize could be awarded.
Step 4:
So, the total number of ways first, second, and third prizes can be awarded is .
Final Answer:

Return to Sample Exam

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