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In this question we're given a standard type of 52 playing cards and you're given 5 cards from the deck.
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In part a, you want to find the number of different 5 card combinations or called poker hands.
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Take note the 5 cards are selected without replacement.
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And after they are selected, they are not arranged in any particular order.
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So the order of selection is not important.
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Without replacement order not important will be using combination.
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That is, if i have n distinct objects and i choose r of them, it will be end.
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V.
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Factoria over r factorial times n minus r factorial.
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So the number of five card combinations that we can have would be from the 52 blank cards we choose five.
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Now using the formula or using your calculator you will get this many number of cards, always a combination of five cards.
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In b, want to find the number of combination where all the cards have the same suit.
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That means there's our huts, all clubs, all spades, or all diamonds.
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So that will be from the four suits, we choose one.
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Now, n is times, all is plus...