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15. a) How many cards must be chosen from a standard deck
of 52 cards to guarantee that at least two of the four
aces are chosen?
b) How many cards must be chosen from a standard deck
of 52 cards to guarantee that at least two of the four
aces and at least two of the 13 kinds are chosen?
c) How many cards must be chosen from a standard deck
of 52 cards to guarantee that there are at least two cards
of the same kind?
d) How many cards must be chosen from a standard deck
of 52 cards to guarantee that there are at least two cards
of each of two different kinds?
in Combinatory 172 views
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a) 50 (the first 48 are all non-aces, the last two has to be aces)
b) 50 for the two aces (from above); for 2 of 13 kinds you need 5 (4 of 1 kind, 1 of second kind); so you need the bigger number which is 50
c) 14 (13 card which is one of each kind, 14th card has to match one of the 13 kinds)
d) 17 (13 card which is one of each kind, 3 more of one kind for a total of 4 cards of one kind, 1 more of any kind)

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