Question

If $A_{(i,j)}$ be the coefficient of $a^i{b}^j{c}^{2010-i-j}$ in the expansion of $(a+b-c{)}^{2010}$ then

• A. $A_{i,i}$ is defined for $i?1010$
• B. $A_{i,j}=A_{j,i}$
• C. $A{.}_{2i,3i}$ is defined for $i?405$
• D. $A_{0,1}=2000$

Answer 1

The correct option is B $A_{i,j}=A_{j,i}$

Clearly, $A_{i,j}=\frac{2010!}{i!j!(2010-i-j)!}$
$A_{j,i}=\frac{2010!}{j!i!(2010-i-j)!}$
Hence, $A_{i,j}=A_{j,i}$