1.

"^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*18C_(10)+....^(40)C_(10)*^(10)C_(10) is equal to

Answer»

`"^(51)C_(41)`
`"^(50)C_(40)`
`"^(51)C_(21)`
`"^(50)C_(40)`

Solution :`(a)` `'^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*^(18)C_(10)+....^(40)C_(2)*^(10)C_(10)`
`="coefficient of " x^(10) " in" (1-x)^(-11)(1-x)^(-31)`
`="coefficient of " x^(10) " in" (1-x)^(-42)`
`='^(42+10-1)C_(42-1)=^(51)C_(41)=^(51)C_(10)`


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