The coefficient of $x^{3}, y^{4}, z$ in the expansion of ${(1 + x - y + z)}^{10}$ is

12600

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6300

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25200

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None of these

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Solution

The correct option is A $12600$
$(1 + x - y + z)^{10}$
Coefficient, of $x^{3} y^{4} z^{1} {.1}^{2}$
$= (- 1)^{4} \frac{10!}{3! .4! .1! .2!}$
$= \frac{10!}{3! .4! .1! .2!}$
$= 12600$

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