CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Passage:
If n is a positive and $$a_{1},\ a_{2},\ a_{3},..a_{m}\in C$$ then
$$(a_{1}+a_{2}+a_{3}+.... +a_{m})^{n}=\displaystyle \Sigma(\frac{n!}{{ n }_{ 1 }!{ n }_{ 2 }!{ n }_{ 3 }!\ldots n_{m}!})a_{1}^{{ n }_{ 1 }}a_{2}^{{ n }_{ 2 }}a_{3}^{{ n }_{ 3 }}....a_{m}^{{ n }_{ m }}$$
where $$n_{1},n_{2},\ n_{3},\ n_{m}$$ are all non negative integers subject to the condition 
$$n_{1}+n_{2}+n_{3}+\ldots+n_{m}=n$$
The coefficient of $$x^{3}y^{4}z$$ in the expansion of $$(1+x-y+z)^{9}$$ is


A
2320
loader
B
2420
loader
C
2520
loader
D
2620
loader

Solution

The correct option is D $$2520$$
The coefficient of $$x^3 y^4 z$$ will be $$\dfrac{9!}{3!4!1!(9-(4+3+1))!}$$.
$$=\dfrac{9!}{3!4!1!1!}$$
$$=\dfrac{9.8.7.6.5}{3!}$$
$$=9.8.7.5$$
$$=40.9.7$$
$$=360.7$$
$$=2520$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image