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Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. How many ways can a hand of five cards consisting of three cards from one suit and two cards from another suit be drawn from a standard deck of cards?
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Oregon State University
We don’t have your requested question, but here is a suggested video that might help.
Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. How many ways can a hand of five cards consisting of three cards from one suit and two cards from another suit be drawn from a standard deck of cards?
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So, I am having a problem with this in that the method I use gives two completely separate answers.
Two cards are selected from a deck of $52$ playing cards. What is the probability they constitute a pair (that is, that they are of the same denomination)?
So, for the first method I reason this.
The first card picked has a $13/52$ chance of being in some suit. The second card picked has probability $12/51$ of being in the same suit.
So... The probability should be $(13/52)(12/52) = 3/52$.
The other method is by combinatorics.
I have $52 \cdot 51$ one ways of creating a pair of cards. But I have $13 \cdot 12$ different ways of creating a pair of the same suit. Now to me, the logical thing to do is to multiply this number by $4$, because I would have to count each valid pair from each suit.
This would give me
$$\frac{4 \cdot 12 \cdot 13}{52 \cdot 51}$$
What's wrong with the reasoning on the second one?