2008 AMC 12B Problems/Problem 1
Contents
Problem
A basketball player made baskets during a game. Each basket was worth either or points. How many different numbers could represent the total points scored by the player?
Solution 1
If the basketball player makes three-point shots and two-point shots, he scores points. Clearly every value of yields a different number of total points. Since he can make any number of three-point shots between and inclusive, the number of different point totals is .
Solution 2
Stars and bars can also be utilized to solve this problem. Since we need to decide what number of 2's and 3's are scored, and there are a total of 5 shots. It can be written like such: _ _ _ | _ _. Solving this, we get .
See Also
2008 AMC 12B (Problems • Answer Key • Resources) | |
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Followed by Problem 2 |
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