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Oregon State University
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?
Get the answer to your homework problem. Try Numerade free for 7 days
Oregon State University
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?
Want to improve this question? Add details and clarify the problem by editing this post. So, I am having a problem with this in that the method I use gives two completely separate answers.
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? |