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Relation between Coefficient and Indices of x and y

Find the coef...

Question

Find the coefficient of $x^{2} y^{2} z$ in the multiple expansion of $(x + y + z)^{5}$ .

30

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40

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50

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60

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Solution

The correct option is A $30$
The general term in the expansion of $(x + y + z)^{5}$ is $\frac{5!}{m! n! t!} x^{m} y^{n} z^{t}$
So the coefficient of $x^{2} y^{2} z$ is $\frac{5!}{2! 2! 2!} = 30$
Therefore the correct option is $A$

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Similar questions

28.5

x

y

Class-interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
Frequency	$5$	$x$	$20$	$15$	$y$	$5$	$60$

46

x

y

230

Class Interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Number of students	$12$	$30$	x	$65$	y	$25$	$18$

x

y

31

$C I$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
Frequency	$5$	$x$	$6$	$y$	$6$	$5$	$40$

(x + y + z)^{5}

(x + y + z)^{n}

^{n + 2} C_{2}

x^{40}

(1 + 2 x + x^{2})^{27}

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