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If A(i,j) be the coefficient of a^i b^j ...

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`

A

(a) `A_(i,i)` is defined for `i ge 1010`

B

(b) `A_(i,j)=A_(j,i)`

C

(c) `A_(2i,3i)` is defined for `i ge 405`

D

(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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