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Omni-MATH / Let π be a uniformly random permutation of the set {1,2,…,100}. The probability that π²⁰(20)= 20 and π²¹(21)=21 can be expressed as (a)/(b), where a and b are relatively prime posi…

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problem

Let π\pi be a uniformly random permutation of the set {1,2,…,100}\{1,2, \ldots, 100\}. The probability that π20(20)=\pi^{20}(20)= 20 and π21(21)=21\pi^{21}(21)=21 can be expressed as ab\frac{a}{b}, where aa and bb are relatively prime positive integers. Compute 100a+b100 a+b. (Here, πk\pi^{k} means π\pi iterated kk times.)
Plain-text mathematical notation (without MathML)
Let π be a uniformly random permutation of the set {1,2,…,100}. The probability that π²⁰(20)= 20 and π²¹(21)=21 can be expressed as (a)/(b), where a and b are relatively prime positive integers. Compute 100a+b. (Here, π^(k) means π iterated k times.)
Original LaTeX notation
Let $\pi$ be a uniformly random permutation of the set $\{1,2, \ldots, 100\}$. The probability that $\pi^{20}(20)=$ 20 and $\pi^{21}(21)=21$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a+b$. (Here, $\pi^{k}$ means $\pi$ iterated $k$ times.)

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Source and history

task_id
6e1ddf6d-0027-500b-b46c-5a0f1b51ff86
task_key
test--6e1ddf6d-0027-500b-b46c-5a0f1b51ff86
task_revision_id
1
config / split
/ test

Official source

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