Problem 5 · AMC 8 Stretch
Core
Counting & Probability
and-process-multiplyconsidering-extreme-cases
Ms. Streett will tip a coat-check helper using coins in her purse: 2 dimes, 2 quarters, and 1 nickel. She will definitely give at least one coin. In how many different ways can she choose which coins to give?
Show answer
Answer: 17 ways
Show hints
Hint 1 of 3
Count by how many of each kind you give, since the two dimes match and the two quarters match.
Still stuck? Show hint 2 →
Hint 2 of 3
Dimes: 0, 1, or 2 (3 choices). Quarters: 0, 1, or 2 (3 choices). Nickel: 0 or 1 (2 choices). Multiply.
Still stuck? Show hint 3 →
Hint 3 of 3
After multiplying, remember she gives at least one coin, so remove the 'give nothing' case.
Show solution
Approach: AND process by quantity, then subtract the empty case
- Count by how many of each kind she gives (an AND process).
- Dimes: 0, 1, or 2 gives 3 ways. Quarters: 0, 1, or 2 gives 3 ways. Nickel: 0 or 1 gives 2 ways.
- Multiply: \(3 \times 3 \times 2 = 18\).
- She definitely tips, so drop the 'give nothing' case: \(18 - 1 = 17\) ways.
Mark:
· log in to save