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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`

Text Solution

Verified by Experts

The correct Answer is:
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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