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Binomial Theorem

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?

Binomial Theorem - Expansions


What is the sum of the coefficients of the terms in \((x-3)^4\) when expanded?

For what value of \(n \geq 24 \) are the coefficients of \(x^{14}\) and \(x^{24}\) equal in the expansion of \((1+x)^{n}\)?

Expand \[(x+1)(x^2-y)^{18}\] and determine the absolute value of the coefficient of \(x^{31}y^3\).

What is the coefficient of the \(x^3\) term in the expansion of \(\left((x+1)^ 2\right)^ {5}\)?

The coefficient of \(x^{9}y^3\) in the expansion of \((x+ay)^{12}\) is \(27500\). What is the value of \(a\)?


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