1. **Problem statement:** From a standard 52-card deck, how many cards must be chosen at random to guarantee having at least three cards of clubs? 2. **Understanding the problem:** A standard deck has 52 cards divided into 4 suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards. 3. **Goal:** Find the minimum number of cards to pick to be sure of having at least 3 clubs. 4. **Approach:** Use the pigeonhole principle. To guarantee 3 clubs, consider the worst case where you pick as many non-club cards as possible before getting 3 clubs. 5. **Calculation:** - Maximum non-club cards = 52 - 13 = 39 - Maximum clubs before having 3 clubs = 2 6. **Total cards to guarantee 3 clubs:** $$ 39 \text{ (non-clubs)} + 2 \text{ (clubs)} + 1 = 42 $$ 7. **Explanation:** If you pick 41 cards, you could have 39 non-clubs and 2 clubs, so not guaranteed 3 clubs yet. But at 42 cards, you must have at least 3 clubs. **Final answer:** $$\boxed{42}$$