The binomial coefficient \(\binom{n}{i+1}\) is commonly expressed as:

\[
\binom{n}{i+1} = \frac{n!}{(i+1)!(n-(i+1))!} = \frac{n!}{(i+1)!(n-i-1)!}
\]

where:

- \( n! \) is the factorial of \(n\),
- \( (i+1)! \) is the factorial of \(i+1\),


Learn how to calculate the binomial coefficient \binom{n}{i+1} using factorials. This problem covers essential combinatorics concepts, including binomial coefficients and the Binomial Theorem, suitable for students in Grades 10-12.

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