41. The exponential factorials grow much more quickly than regular factorials or even hyperfactorials. 42. The last one should be 24, which suggests factorials or something similar. 43. The series is a sum of factorials that alternatingly are added or subtracted. 44. After you work out the probability using derangement, partial derangement and factorial . 45. Under these conditions, we may use Stirling's approximation for the factorial : 46. Because of this, R . A Fisher popularized the use of factorial designs. 47. General properties of mixed radix number systems also apply to the factorial number system. 48. For the vast majority of factorial experiments, each factor has only two levels. 49. The denominator there is just to cut the factorial off after a certain amount. 50. An orthogonal array of strength 2 can be used to design a factorial experiment.