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If a coin comes up heads you win $10, but if it comes up tails you win $0. How likely are you to win exactly $30 in five flips?

What positive integer \(n\) satisfies \[{{n+2} \choose 11}=109 \cdot {n \choose 9}?\]

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What is the value of positive integer \(n\) satisfying \[{26 \choose n}={26 \choose {n-4}}?\]

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If \({n+4 \choose 2}+{n+3 \choose 2}=25,\) what is the value of \(n?\)

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