Problem 16 · AMC 8 Stretch
Stretch
Counting & Probability
or-process-addlogical-reasoning
Brenda will borrow either 2 or 3 books from a stack of 5 books. In how many ways can she make her selection?
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Answer: 20 ways
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Hint 1 of 4
The word 'or' is the clue. She borrows exactly 2 OR exactly 3 — she can't do both at once, so this is an OR (add) process.
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Hint 2 of 4
Count the ways to pick exactly 2 of the 5 books, then separately the ways to pick exactly 3.
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Hint 3 of 4
Ways to pick 2 of 5: list them or use 'choose 2'. Ways to pick 3 of 5 is the same as choosing which 2 to leave out. Add the two counts.
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Approach: OR process — add the two non-overlapping cases
- This is an OR process: she takes exactly 2 OR exactly 3 books, and these can't happen together.
- Ways to choose 2 of 5 books: there are 10 (you can list the pairs).
- Ways to choose 3 of 5 books: choosing 3 to take is the same as choosing the 2 to leave behind, so this is also 10.
- The two cases don't overlap, so add: \(10 + 10 = 20\).
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