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
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 ge 1010`
B. `A_(i,j)=A_(j,i)`
C. `A_(2i,3i)` is defined for `i ge 405`
D. `A_(0,1)=2000`
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Correct Answer - B
`(b)` Clearly `a_(i,j)=(2010!)/(i!j!(2010-i-j)!)`
and `a_(j,i)=(2010!)/(j!i!(2010-i-j)!)`
Hence , `a_(i,j)=a_(j,i)`
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