Intereting Posts

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Is there a non-trivial example of a $\mathbb Q-$endomorphism of $\mathbb R$?
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Check Points are line, triangle, circle or rectangle
How to prove $\log n < n$?
Find the remainder using Fermat's little theorem when $5^{119}$ is divided by $59$?
Product of $SU(2)$ representations
Is there a closed form for the infinite product $\prod_{n=0}^{\infty}\bigl(1+{x \over 2^n} \bigr)$
Find a non-negative function on such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
How to prove $\deg( f\circ g) = \deg(f) \deg(g) $?
Limit of $\sqrt{x^2-6x+7}-x$ as x approaches negative infinity
Does the set of $m \in Max(ord_n(k))$ for every $n$ without primitive roots contain a pair of primes $p_1+p_2=n$?

Let A be a set of n distinct elements, and let A’ and A” be independent permutations of A, where |A’| = |A”| = k. What is the expectation for |A’ ∩ A”| for any given k <= n?

- how to find the root of permutation
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- The number of regions into which a plane is divided by n lines in generic position
- Finding the order of permutations in $S_8$

By linearity of expectation, the expectation value is $n$ times the probability that any given element of $A$ is in both sets. The probability for that is $(k/n)^2$, so the desired expectation value is $k^2/n$.

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- Showing that $M$ and $N$ will have same eigenvalues.