If coefficient of a2b3c4 in (a+b+c)m (where m ∈ N) is L (L≠0), then in same expansion coefficient of a4b4c1 will be

Question

If coefficient of a2b3c4 in (a+b+c)m (where m ∈ N) is L (L≠0), then in same expansion coefficient of a4b4c1 will be (A) L (B) (L/3) (C) (mL/4) (D) (L/2)

Tardigrade Admin · Accepted Answer

As L≠0 ∴ m=2+3+4=9 ∴ L=(9!/2!3!4!) Now coefficient of a4 b4 c =(9!/4!4!1!)=(L/2)

Q. If coefficient of $a^{2} b^{3} c^{4}$ in $(a + b + c)^{m}$ (where m $\in N$ ) is $L (L \neq = 0),$ then in same expansion coefficient of $a^{4} b^{4} c^{1}$ will be

$L$

$\frac{L}{3}$

$\frac{m L}{4}$

$\frac{L}{2}$

$A s L \neq = 0$
$∴ m = 2 + 3 + 4 = 9$
$∴ L = \frac{9 !}{2 ! 3 ! 4 !}$
Now coefficient of $a^{4} b^{4} c = \frac{9 !}{4 ! 4 ! 1 !} = \frac{L}{2}$

Q. If coefficient of a2b3c4 in (a+b+c)m (where m ∈N) is L(L=0), then in same expansion coefficient of a4b4c1 will be

L

3L​

4mL​

2L​

AsL=0 ∴m=2+3+4=9 ∴L=2!3!4!9!​ Now coefficient of a4b4c=4!4!1!9!​=2L​

Q. If coefficient of $a^{2} b^{3} c^{4}$ in $(a + b + c)^{m}$ (where m $\in N$ ) is $L (L \neq = 0),$ then in same expansion coefficient of $a^{4} b^{4} c^{1}$ will be

$L$

$\frac{L}{3}$

$\frac{m L}{4}$

$\frac{L}{2}$

$A s L \neq = 0$
$∴ m = 2 + 3 + 4 = 9$
$∴ L = \frac{9 !}{2 ! 3 ! 4 !}$
Now coefficient of $a^{4} b^{4} c = \frac{9 !}{4 ! 4 ! 1 !} = \frac{L}{2}$