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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?

Evaluate \[{42 \choose 40}.\]

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What value of \(n\) satisfies \[{n \choose 2}=465?\]

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What is the coefficient of \( x^ 5 \) in the expansion of \( (x+1)^ {8} \)?

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What is the value of positive integer \(n\) satisfying \[{22 \choose n}={22 \choose {n-10}}?\]

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What is the coefficient of the \(x^ 4 y^ 4\) term in the expansion of \((x+y)^{8}\)?

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