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  4. 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

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Q. If coefficient of $a^{2}b^{3}c^{4}$ in $(a+b+c)^{m}$ (where m $\in N$) is $L \left(L\ne0\right),$ then in same expansion coefficient of $a^{4}b^{4}c^{1}$ will be

Binomial Theorem

Solution:

$As L\ne0$
$ \therefore m=2+3+4=9 $
$\therefore L=\frac{9!}{2!3!4!} $
Now coefficient of $a^{4} b^{4} c =\frac{9!}{4!4!1!}=\frac{L}{2}$