Difference between revisions of "004 Sample Final A, Problem 18"
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! Foundations | ! Foundations | ||
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| − | | | + | |If there are n teams, how many ways can first prize be awarded? |
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|Answer: | |Answer: | ||
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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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! Step 1: | ! Step 1: | ||
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| − | | | + | |There are 10 ways that first prize could be awarded. |
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! Step 2: | ! Step 2: | ||
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| − | | | + | |After choosing a first place winner, there are 9 ways that second prize could be awarded. |
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! Step 3: | ! Step 3: | ||
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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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! Step 4: | ! Step 4: | ||
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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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! Final Answer: | ! Final Answer: | ||
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| − | | | + | |<math>720</math> |
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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 15:28, 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: |
|---|
