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Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)...

Evaluate `|{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|`

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The correct Answer is:
`(1)/(12)xyz(x-y)(y-z)(z-x)`
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