Browse Questions

# $\large\frac{^8C_0}{6}$ - $^8C_1$ + $^8C_2.6$ + $....$ + $^8C_8.6^7$ = ?

$\begin{array}{1 1} 0 \\ 6^7 \\ 6^8 \\ \frac{5^8}{6} \end{array}$

$(1-x)^8=^8C_0-^8C_1x+^8C_2.x^2-^8C_3x^3+.......^8C_8x^8$
$\large\frac{(1-x)^8}{x}$$=\large\frac{^8C_0}{x}$$-^8C_1+^8C_2.x-.........+^8C_8.x^7$
By putting $x=6$ on both the sides we get
$\large\frac{(1-6)^8}{6}$$=\large\frac{^8C_0}{6}$$-^8C_1+^8C_2.6-.........+^8C_8.6^7$
$=\large\frac{5^8}{6}$