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Mar
10
awarded  Famous Question
Mar
8
comment Ball Permutations without replacement
This makes sense given that the all of the colors have the same number of balls. How would the answer change if, for example, we instead had 13 yellow, 17 red, 14 white, and 16 green balls?
Mar
8
comment Ball Permutations without replacement
@lulu - I'm in the same class, I think that might be a strong possibility. I got the answer from the professor (but no explanation with it) and she said the answer was $$\frac{\binom{15}{5}\binom{15}{4}\binom{15}{3}4!}{\binom{60}{14}}$$. But I didn't understand how this answer worked given the constraints listed above.
Dec
26
awarded  Good Question
Dec
26
awarded  Notable Question
Dec
24
accepted Picking two random real numbers between 0 and 1, why isn't the probability that the first is greater than the second exactly 50%?
Dec
24
awarded  Popular Question
Dec
24
revised Picking two random real numbers between 0 and 1, why isn't the probability that the first is greater than the second exactly 50%?
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Dec
24
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Dec
24
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Dec
24
revised What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
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Dec
24
comment What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
In the analogy, if I all of my rocks have a unique rock from your set next to it, the mapping is injective. If all of your rocks have a unique rock from my set of rocks next to it, the function is surjective. If both are true, the function is bijective. But if I am able to line up your rocks in such a way that all of them have a unique rock of mine next to them, and then I have some left over, it would normally imply that I have more rocks.
Dec
24
comment What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
I guess the reason I am confused is because the intuition is no longer there. The argument for finite sets can be easily explained as a way to count without numbers. For example, if you and I have a bunch of rocks, and you want to see who has more, you can line them up, and see who has left over at the end. If all of mine have one of your rocks next to it, but I have some left over, I have more. If all of your rocks has one of mine next to it, but you have left over, you have more. If there are none left over on either side, they are equal. But this no longer seems to work for infinite sets.
Dec
24
comment What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
Actually, the maping $\mathbb{B} \rightarrow \mathbb{A} : x \rightarrow \frac{x}{2}$ would be bijective, since everything in $\mathbb{A}$ is also in $\mathbb{B}$. But the mapping $\mathbb{A} \rightarrow \mathbb{B} : x \rightarrow x$ is strictly injective. An injective function may imply that $A \leq B$, but the lack of surjectivity would seem to negate the $=$ part - implying $A < B$
Dec
24
revised What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
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Dec
24
asked What does a one-to-one mapping say about the cardinality of the reals if it isn't onto?
Dec
24
revised Picking two random real numbers between 0 and 1, why isn't the probability that the first is greater than the second exactly 50%?
added 10 characters in body
Dec
24
asked What is the probability that a random integer is greater than $n$?
Dec
24
revised Picking two random real numbers between 0 and 1, why isn't the probability that the first is greater than the second exactly 50%?
added 44 characters in body
Dec
24
asked Picking two random real numbers between 0 and 1, why isn't the probability that the first is greater than the second exactly 50%?