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Omni-MATH / Let a,b be integers chosen independently and uniformly at random from the set {0,1,2,…,80}. Compute the expected value of the remainder when the binomial coefficient …

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problem

Let a,ba, b be integers chosen independently and uniformly at random from the set {0,1,2,…,80}\{0,1,2, \ldots, 80\}. Compute the expected value of the remainder when the binomial coefficient $\binom{a}{b}=\frac{a!}{b!(a-b)!}$ is divided by 3.
Plain-text mathematical notation (without MathML)
Let a,b be integers chosen independently and uniformly at random from the set {0,1,2,…,80}. Compute the expected value of the remainder when the binomial coefficient $\binom{a}{b}=\frac{a!}{b!(a-b)!}$ is divided by 3.
Original LaTeX notation
Let $a, b$ be integers chosen independently and uniformly at random from the set $\{0,1,2, \ldots, 80\}$. Compute the expected value of the remainder when the binomial coefficient $\binom{a}{b}=\frac{a!}{b!(a-b)!}$ is divided by 3.

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Source and history

task_id
8bde7681-22af-5eae-b291-35f3cb57fdd8
task_key
test--8bde7681-22af-5eae-b291-35f3cb57fdd8
task_revision_id
1
config / split
/ test

Official source

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