Question

Find the value of each expression. Show your work. 10^C^4

Answer 1

$_nC_r = \frac{n!}{(n - r)!r!}$
$_1_0C_4 = \frac{10!}{(10 - 4)!4!}$
$_1_0C_4 = \frac{10!}{6!4!}$
$_1_0C_4 = \frac{10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1}{6 * 5 * 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1}$
$_1_0C_4 = \frac{10 * 9 * 8 * 7}{4 * 3 * 2 * 1}$
$_1_0C_4 = \frac{90 * 56}{12 * 2}$
$_1_0C_4 = \frac{5040}{24}$
$_1_0C_4 = 210$