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2. (Math Question) Minimum number of cards needs to be drawn
How many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same suit are chosen?
Pick ONE option
Show answer & explanation
Answer: C. 9
This is a pigeonhole principle problem. A standard deck has 4 suits. To guarantee at least 3 cards of the same suit, we must account for the worst-case scenario: drawing exactly 2 cards from each of the 4 suits first (total 8 cards), then the 9th card must give us a third card of some suit.
Step-by-step Derivation:
By the pigeonhole principle:
- There are 4 suits in a standard deck
- Worst case: we draw 2 cards from each suit = 2 × 4 = 8 cards (we still don't have 3 of any suit)
- The next card (9th card) must belong to one of the 4 suits, giving us 3 cards of that suit
- Therefore, minimum cards needed = 8 + 1 = 9 cards
General formula: To guarantee n cards of the same suit with s suits, we need (n-1) × s + 1 = (3-1) × 4 + 1 = 2 × 4 + 1 = 9