The coefficient of 8th term in the expansion of(1+x)10 is

Given expansion of ${(1 + x)}^{10}$ is

We have general term in the expansion ${(x + a)}^{n}$

$(∴ T_{r + 1} =^{n} C_{r} x^{n - r} {(a)}^{r}$ be the expansion of ${(x + a)}^{n})$

$8^{t h}$ term:

$T_{r + 1} =^{n} C_{r} x^{n - r} {(a)}^{r}$

$T_{8} = T_{7 + 1} =^{10} C_{7} {(1)}^{10 - 7} {(x)}^{7}$

coefficient $x^{7}$ in $T_{8} = T_{7 + 1} =^{10} C_{7}$ $\begin{matrix} (∴^{n} C_{r} = \frac{n!}{(n - r)! r!}) \end{matrix}$

$= \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 (^{10} C_{7} =^{10} C_{3})$

The coefficient of $8^{t h}$ term in the expansion of ${(1 + x)}^{10}$ is