Answer
$W = 9.25 \times 10^{58}$
Work Step by Step
To find the multiplicity, W of the central configuration,
$N = 200, $ Since the sample is divided into two halves, $n_1 = 100, n_2 = 100$
$W = \frac{N!}{n_1!n_2!}$
$W = \frac{200!}{100!100!}$
$W = 9.25 \times 10^{58}$