The number of terms in the expansion of ${(1 + 3 x + 3 x^{2} + x^{3})}^{6}$ is

18

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9

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19

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24

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Solution

The correct option is C $19$
$(1 + 3 x + 3 x^{2} + x^{3})^{6}$
$= [(1 + x)^{3}]^{6}$
$= [1 + x]^{6 (3)}$
$= (1 + x)^{18}$
Hence total number of terms will be $18 + 1 = 19 t e r m s$

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