Find the coefficient of $x^{17}$ in $(x + y)^{20}$ ?

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Solution

Coefficient of $x^{17}$ in $(a + b x)^{n}$ is $^{n} C_{r}$ $b^{r} a^{n - r}$
Coefficient of $x^{17}$ in $(y + x)^{20}$ is $^{20} C_{17}$ $y^{20 - 17}$
$= 1140 y^{3}$

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Find the coefficient of $x^{17}$ in the expansion $(x + x^{2} + x^{3} + . . . . . . . . . . . . . . x^{6})^{6} (1 + x + x^{2} + x^{3} + . . . . . . . . .)$

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Find the coefficient of x17 in (x+y)20 ?

Coefficient of x17 in (a+bx)n is nCr bran−rCoefficient of x17 in (y+x)20 is 20C17 y20−17 =1140y3

Find the coefficient of $x^{17}$ in $(x + y)^{20}$ ?

Coefficient of $x^{17}$ in $(a + b x)^{n}$ is $^{n} C_{r}$ $b^{r} a^{n - r}$
Coefficient of $x^{17}$ in $(y + x)^{20}$ is $^{20} C_{17}$ $y^{20 - 17}$
$= 1140 y^{3}$