1.

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____".

Answer»


SOLUTION :`underset(r=0)overset(3)sum.^(8)(C_(r+1)-.^(4)C_(r))=underset(r=0)overset(3)sum.^(8)C_(r).^(4)C_(r+1)`
`= .^(8)C_(0) XX.^(4)C_(1)+.^(8)C_(1)xx.^(4)C_(2)+.^(8)C_(2)xx.^(4)C_(3)+.^(8)C_(3)xx.^(4)C_(4)`
`=` coefficient of `x^(3)` in `(1+x)^(4)(1+x)^(8)`
`=` coeficient of `x^(3)` in `(1+x)^(12)`
`=.^(12)C_(3) = 220`


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