Problem 15 · AMC 8 Stretch
Core
Counting & Probability
and-process-multiplyconsidering-extreme-cases
Mrs. Stux has 3 dimes, 2 quarters, and 4 nickels in her purse. She will give a tip of one or more coins. How many different tips can she give? (Count by how many of each kind she uses.)
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Answer: 59 tips
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Hint 1 of 3
Coins of the same kind look alike, so count by how many of each kind you give.
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Hint 2 of 3
Dimes: 0-3, quarters: 0-2, nickels: 0-4. Find the number of choices for each, then multiply.
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Hint 3 of 3
Dimes 4 ways, quarters 3 ways, nickels 5 ways. After multiplying, subtract the 'no tip' case since she gives one or more.
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Approach: AND process by quantity, then subtract the empty case
- Count by how many of each kind she gives (AND process).
- Dimes: 0-3 gives 4 ways. Quarters: 0-2 gives 3 ways. Nickels: 0-4 gives 5 ways. So \(4 \times 3 \times 5 = 60\).
- She gives one or more coins, so subtract the empty tip: \(60 - 1 = 59\).
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