# Tagged Questions

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### Ball Probability help

A bowl contains 5 red balls, 3 white balls and 2 blue balls. Two balls are seleceted at random from the bowl (without replacement). A) What is the probability that both are red? which is 2/9 B) What ...
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### Prove $x$ and $y$ in $y = x^2 + 2$ are prime only for $x = 3$ and $y = 11$?

Let $x$ be a positive integer and $y = x^2 + 2$. Can $x$ and $y$ be both prime? The answer is yes, since for $x = 3$ we get $y = 11$, and both numbers are prime. Prove that this is the only value of x ...
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### find the recurrence relation (homework)

I'm new to recurrence relations and I'm having trouble figuring out this problem: Find a recurrence relation for the number of ways to make a stack of green, yellow, and orange napkins so that no two ...
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### Defining a bijective function from $2\mathbb{N}$ to $3\mathbb{Z}-1$?

$2\mathbb{N}=\{2n:n\in\mathbb{N}\}$ and $3\mathbb{Z}-1=\{3n-1:n\in\mathbb{Z}\}$ Work: So far, my plan is to first define a bijective function from $2\mathbb{N}$ to $\mathbb{N}$ and then define ...
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### Proving that function $f:[0,\infty)\rightarrow [0,\infty)$ defined by $f(x)=\frac{x^2}{1-x}$ is bijective.

I am having a bit of trouble with the algebra for proving that the function is injective. Basically I set $f(a)=f(b)$ for $a,b\in[0,\infty)$ and $a,b\neq 1$. ...
I know the number of reflexive relations on a finite set is: $2^{n^{2}-n}$ The number of symmetric relations is: $2^{n+1 \choose 2}$ The number of antisymmetric relations: $2^{n}3^{n \choose 2}$ ...