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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremMultinomial theoremMedium2 minQB

MathematicsMediumsingle choice

The coefficient of $a^{8} b^{6} c^{4}$ in the expansion of $(a + b + c)^{18}$ is :

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Answer:

Solution:

$(a + b + c)^{18} = [a + (b + c)]^{18}$ $=^{18} C_{0} a^{18} +^{18} C_{1} a^{17} (b + c)^{1} +^{18} C_{2} a^{16} (b + c)^{2} + \dots +^{18} C_{10} a^{8} (b + c)^{10} + \dots .$ ∴coefficient of $a^{8} b^{6} c^{4} =^{18} C_{10} \times^{10} C_{6} = \frac{18 !}{8 ! 6 ! 4 !} =^{18} C_{4} \times^{14} C_{6}$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Multinomial theorem

⏱ 2mℹ️ Source: QB

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