HMMT 2011 U33

Guts
Answer

Find the number of sequences consisting of $100 R$ 's and $2011 S$ 's that satisfy the property that among the first $k$ letters, the number of $S$ 's is strictly more than 20 times the number of $R$ 's for all $1 \leq k \leq 2111$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{11}{2111}\binom{2111}{100}

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