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The value of sum(r=0)^(40) r""^(40)C(r)"...

The value of `sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r)` is (a) `40.^(69)C_(29)` (b) `40.^(70)C_(30)` (c) `.^(60)C_(29)` (d) `.^(70)C_(30)`

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The correct Answer is:
A
`underset(r=0)overset(40)sumr.^(40)C_(r).^(30)C_(r)=40underset(r=0)overset(40)sum.^(29)C_(r-1).^(30)C_(r)`
`= 40 underset(r=0)overset(40)sum.^(39)C_(r-1).^(30)C_(30-r)`
`= 40^(39+30)C_(r+1+30-r)`
`= 40.^(69)C_(29)`
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