SOLUTION: How many cards must be drawn from a standard 52 card deck to be certain that 4 cards of the same suit are drawn? Thanks in advance!!!

Question 551256: How many cards must be drawn from a standard 52 card deck to be certain that 4 cards of the same suit are drawn?
Thanks in advance!!!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The 1st 13 cards you draw could all be the
same suit. Not likely, but possible.
If you draw 14 cards, there is zero probability
that they will all be the same suit, and it is certain
you will have at least 2 cards of different suits.
If you draw more cards until you have drawn 26,
it is still possible you have 13 of one suit and
13 of another suit
If you draw one more card to make 27, you know
that you are certain to have at least 3 cards of
different suits.
If you keep drawing until you have 3x13 = 39 cards
it is still possible that you have only cards of 3 suits,
Drawing one more card makes it 100% certain that you
have all 4 suits
So, you must draw 40 cards to know that you have cards
of all 4 suits
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