Ephraim
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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%? edited title Dec 24 awarded Nice Question Dec 24 awarded Yearling Dec 24 revised What does a one-to-one mapping say about the cardinality of the reals if it isn't onto? added 803 characters in body 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? added 52 characters in body 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%?