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Find the value of .^(20)C(0) xx .^(13)...

Find the value of
`.^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10)`.

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`.^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) -"…." + .^(20)C_(10)`
`=` Coefficient of `x^(10)` in
`(.^(20)C_(0) - .^(20)C_(1)x + .^(20)C_(2)x^(2) - .^(20)C_(3)x^(3) + "…..")`
`(1+.^(4)C_(1)x + .^(5)C_(2)x^(2)+.^(6)C_(3)x^(3)+".....")`
`=` Coefficient of `x^(10)` in `(1-x)^(20)(1-x)^(-4)`
`=` Coefficient of `x^(10)` in `(1-x)^(16)`
`= .^(16)C_(10)`.
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