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"^(30)C(0)*^(20)C(10)+^(31)C(1)*^(19)C(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

A

`"^(51)C_(41)`

B

`"^(50)C_(40)`

C

`"^(51)C_(21)`

D

`"^(50)C_(40)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(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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