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Omni-MATH / The English alphabet, which has 26 letters, is randomly permuted. Let p₁ be the probability that AB,CD, and EF all appear as contiguous substrings. Let p₂ be the probability that …

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problem

The English alphabet, which has 26 letters, is randomly permuted. Let p1p_{1} be the probability that AB,CD\mathrm{AB}, \mathrm{CD}, and EF\mathrm{EF} all appear as contiguous substrings. Let p2p_{2} be the probability that ABC\mathrm{ABC} and DEF\mathrm{DEF} both appear as contiguous substrings. Compute p1p2\frac{p_{1}}{p_{2}}.
Plain-text mathematical notation (without MathML)
The English alphabet, which has 26 letters, is randomly permuted. Let p₁ be the probability that AB,CD, and EF all appear as contiguous substrings. Let p₂ be the probability that ABC and DEF both appear as contiguous substrings. Compute (p₁)/(p₂).
Original LaTeX notation
The English alphabet, which has 26 letters, is randomly permuted. Let \(p_{1}\) be the probability that \(\mathrm{AB}, \mathrm{CD}\), and \(\mathrm{EF}\) all appear as contiguous substrings. Let \(p_{2}\) be the probability that \(\mathrm{ABC}\) and \(\mathrm{DEF}\) both appear as contiguous substrings. Compute \(\frac{p_{1}}{p_{2}}\).

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Source and history

task_id
2b94c20b-2e32-5a69-9e09-965461c08a66
task_key
test--2b94c20b-2e32-5a69-9e09-965461c08a66
task_revision_id
1
config / split
/ test

Official source

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