Let $z \in \mathbb{C}$ and if $A = \{z : \arg(z) = \frac{\pi}{4}\}$ and $B = \{z : \arg(z - 3 - 3i) = \frac{2\pi}{3}\}$. Then $n(A \cap B)$ is equal to:
Step-by-Step Solution
Key Concept: Understanding different representations and properties of binomial coefficients, including Pascal's identity.
The correct representation of binomial coefficients is $^nC_r$. Option (A) shows $^nC_r$ which is the standard notation. Option (B) shows the formula $\frac{n}{r(n-r)} = ^nC_r$ with specific values listed. Option (C) shows $^{n+1}C_r$ which represents a different binomial coefficient. Option (D) shows the Pascal's triangle identity $^{n-1}C_{r-1} + ^{n-1}C_r = ^nC_r$.
Correct Answer: 2,4