Evaluate the following without using a calculator \(\left( \begin{matrix} 8 \ 3 \ \end{matrix} \ri

Question

Evaluate the following without using a calculator $\left( \begin{matrix} 8 \ 3 \ \end{matrix} \right)$ $\left( \begin{matrix} 5 \ 2 \ \end{matrix} \right)$ $\left( \begin{matrix} n+1 \ 4 \ \end{matrix} \right)$ in terms of $n$ $\left( \begin{matrix} n \ 1 \ \end{matrix} \right)$ in terms of $n$ $\left( \begin{matrix} n+1 \ n \ \end{matrix} \right)$ in terms of $n$ $\left( \begin{matrix} n \ n \ \end{matrix} \right)$ in terms of $n$ $\left( \begin{matrix} n \ 0 \ \end{matrix} \right)$ in terms of $n$

Accepted Answer

(a) $56$; (b) $10$; (c) $\dfrac{(n+1)n(n-1)(n-2)}{24}$; (d) $n$; (e) $n+1$; (f) $1$; (g) $1$.

Binomial Theorem - Binomial Coefficients and Pascal's Triangle

Binomial Theorem - Binomial Coefficients and Pascal's Triangle

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