Consider an ordinary deck of 52 playing cards with four suits (hearts, spades, diamonds, clubs) and 13 ranks in each suit (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). You pick cards from the deck one at a time without replacement. What is the minimum number of cards you must pick in order to guarantee that you get: a) a pair of any rank, b) two aces, and c) all four aces.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Consider an ordinary deck of 52 playing cards with four suits (hearts, spades, diamonds,
clubs) and 13 ranks in each suit (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). You pick cards from the deck one
at a time without replacement. What is the minimum number of cards you must pick in order to
guarantee that you get:
a) a pair of any rank,
b) two aces, and
c) all four aces.

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